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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+10x^2+4x-25x-10)+12=0

We get rid of parentheses

10x^2+4x-25x-10+12=0

We add all the numbers together, and all the variables

10x^2-21x+2=0

a = 10; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·10·2
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-19}{2*10}=\frac{2}{20}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+19}{2*10}=\frac{40}{20}
=2
$