Question

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

Answer 1

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

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

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

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

$Discreminant (D) = b^{2} - 4ac \\= 4^{2} - 4 \times 2 \times (-5) \\= 16 + 40 \\= 56 \: --(1)$

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

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

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

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

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

$\implies x = \frac{ -2 \pm \sqrt{14}}{2}$

Therefore.,

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

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