(x-2)=2x^2-7x-24

Solution for (x-2)=2x^2-7x-24 equation:

(x-2)=2x^2-7x-24

We move all terms to the left:

(x-2)-(2x^2-7x-24)=0

We get rid of parentheses

-2x^2+x+7x-2+24=0

We add all the numbers together, and all the variables

-2x^2+8x+22=0

a = -2; b = 8; c = +22;
Δ = b2-4ac
Δ = 82-4·(-2)·22
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{15}}{2*-2}=\frac{-8-4\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{15}}{2*-2}=\frac{-8+4\sqrt{15}}{-4}
$