Question

3xsquare +x -7= 4x, solve for x​

Answer 1

Answer:

$\large{\underline{\boxed{\sf x = \frac{3 + \sqrt{93} }{6} \: \: or \: \: x = \frac{3 - \sqrt{93} }{6}}}}$

Step-by-step explanation:

3x² + x - 7 = 4x

⇒ 3x² + x - 4x - 7 = 0

⇒ 3x² - 3x - 7 = 0

On comparing the given equation with the standard form of quadratic equation ax² + bx + c = 0,

a = 3, b = - 3, c = - 7

Discriminant = b² - 4ac

⇒ D = (-3)² - 4 * 3 * (-7)

⇒ D = 9 + 84

⇒ D = 93

$\tt x = \frac{ - b \pm \sqrt{d} }{2a} \\ \\ \tt x = \frac{ - ( - 3) \pm \sqrt{93} }{2 \times 3} \\ \\ \tt x = \frac{3 \pm \sqrt{93} }{6} \\ \\ \bf \therefore x = \frac{3 + \sqrt{93} }{6} \: \: or \: \: x = \frac{3 - \sqrt{93} }{6}$

Answer 2

Answer:

$\huge{\red{\boxed{\boxed{\green{\sf{\therefore x=\frac{3+\sqrt{93}}{6},\frac{3-\sqrt{93}}{6}}}}}}}$

Step-by-step explanation:

$\huge{\red{\boxed{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}}$

□3x^2+x-7=4x

To find:

○value of x=?

$3 {x}^{2} + x - 7 = 4x \\ take \: all \: the \: variable \: in \: left \: side \\ 3 {x}^{2} + x - 7 - 4x = 0 \\ = )3 {x}^{2} - 3x - 7 = 0 \\ \\ {\boxed {method \: ( quadratic \: formula)}} \\ > > first \: find \: discriminant \\ \\d = {b}^{2} - 4ac \\ d= { (- 3)}^{2} - 4(3 \times - 7) \\ d = 9 - 4( - 21) \\d = 9 +8 4 \\ d = 93 \\ \\ x = \frac{ - b + - \sqrt{d} }{2a} \\ x = \frac{ - ( - 3) + \sqrt{93} }{2 \times 3} \\\therefore x = \frac{3 + \sqrt{93} }{6} - - - - - 1st \: zeroes \\ \\\therefore x = \frac{ 3 - \sqrt{93} }{6} - - - - - 2nd \: zeroes$

$\huge{\red{\boxed{\boxed{\green{\sf{\therefore x=\frac{3+\sqrt{93}}{6},\frac{3-\sqrt{93}}{6}}}}}}}$

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