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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+10x^2-15x+4x-6)-12=0

We get rid of parentheses

10x^2-15x+4x-6-12=0

We add all the numbers together, and all the variables

10x^2-11x-18=0

a = 10; b = -11; c = -18;
Δ = b2-4ac
Δ = -112-4·10·(-18)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-29}{2*10}=\frac{-18}{20}
=-9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+29}{2*10}=\frac{40}{20}
=2
$