(X-4)2=2x2-9x-14

Solution for (X-4)2=2x2-9x-14 equation:

(X-4)2=2X^2-9X-14

We move all terms to the left:

(X-4)2-(2X^2-9X-14)=0

We multiply parentheses

2X-(2X^2-9X-14)-8=0

We get rid of parentheses

-2X^2+2X+9X+14-8=0

We add all the numbers together, and all the variables

-2X^2+11X+6=0

a = -2; b = 11; c = +6;
Δ = b2-4ac
Δ = 112-4·(-2)·6
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*-2}=\frac{-24}{-4}
=+6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*-2}=\frac{2}{-4}
=-1/2
$