5x(3x-2)=-12x+8

Solution for 5x(3x-2)=-12x+8 equation:

5x(3x-2)=-12x+8

We move all terms to the left:

5x(3x-2)-(-12x+8)=0

We multiply parentheses

15x^2-10x-(-12x+8)=0

We get rid of parentheses

15x^2-10x+12x-8=0

We add all the numbers together, and all the variables

15x^2+2x-8=0

a = 15; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·15·(-8)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*15}=\frac{-24}{30}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*15}=\frac{20}{30}
=2/3
$