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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+10x^2+15x-4x-6)+3=0

We get rid of parentheses

10x^2+15x-4x-6+3=0

We add all the numbers together, and all the variables

10x^2+11x-3=0

a = 10; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·10·(-3)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{241}}{2*10}=\frac{-11-\sqrt{241}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{241}}{2*10}=\frac{-11+\sqrt{241}}{20}
$