Question

Solve equation by formula method: 2x² = 5 - 4x ​

Answer 1

Answer:

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Answer 2

$Given\: Quadratic \: Equation: 2x^{2} = 5 - 4x$

$\implies 2x^{2} + 4x -5 = 0$

/* Compare this equation with ax² + bx + c = 0, we get */

$a = 2 , \: b = 4 \: and \: c = -5$

$Discreminant (D) = b^{2} -4ac \\= 4^{2} - 4 \times 2\times (-5) \\= 16 + 40 \\= 56$

$\underline { \blue { By \: Quadratic\: Formula :}}$

$\boxed{\pink { x = \frac{-b \pm \sqrt{D}}{2a} }}$

$\implies x = \frac{-4 \pm \sqrt{56}}{2\times 2} \\= \frac{-4 \pm 2\sqrt{14}}{4} \\= \frac{2(-2 \pm \sqrt{14})}{4} \\= \frac{-2 \pm \sqrt{14}}{2}$

Therefore.,

$\green { x = \frac{-2 + \sqrt{14}}{2} \: Or \: x = \frac{-2 - \sqrt{14}}{2}}$

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