2(2x-1)=2x^2+5x-12

Solution for 2(2x-1)=2x^2+5x-12 equation:

2(2x-1)=2x^2+5x-12

We move all terms to the left:

2(2x-1)-(2x^2+5x-12)=0

We multiply parentheses

4x-(2x^2+5x-12)-2=0

We get rid of parentheses

-2x^2+4x-5x+12-2=0

We add all the numbers together, and all the variables

-2x^2-1x+10=0

a = -2; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-2)·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-2}=\frac{10}{-4}
=-2+1/2
$