-2x(2x-3)=5x-12

Solution for -2x(2x-3)=5x-12 equation:

-2x(2x-3)=5x-12

We move all terms to the left:

-2x(2x-3)-(5x-12)=0

We multiply parentheses

-4x^2+6x-(5x-12)=0

We get rid of parentheses

-4x^2+6x-5x+12=0

We add all the numbers together, and all the variables

-4x^2+x+12=0

a = -4; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-4)·12
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{193}}{2*-4}=\frac{-1-\sqrt{193}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{193}}{2*-4}=\frac{-1+\sqrt{193}}{-8}
$