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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+5x^2-15x+2x-6)-12=0

We get rid of parentheses

5x^2-15x+2x-6-12=0

We add all the numbers together, and all the variables

5x^2-13x-18=0

a = 5; b = -13; c = -18;
Δ = b2-4ac
Δ = -132-4·5·(-18)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*5}=\frac{36}{10}
=3+3/5
$