(3x-2)*(4x+5)=52

Solution for (3x-2)*(4x+5)=52 equation:

(3x-2)(4x+5)=52

We move all terms to the left:

(3x-2)(4x+5)-(52)=0

We multiply parentheses ..

(+12x^2+15x-8x-10)-52=0

We get rid of parentheses

12x^2+15x-8x-10-52=0

We add all the numbers together, and all the variables

12x^2+7x-62=0

a = 12; b = 7; c = -62;
Δ = b2-4ac
Δ = 72-4·12·(-62)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-55}{2*12}=\frac{-62}{24}
=-2+7/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+55}{2*12}=\frac{48}{24}
=2
$