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

Solution for (2x-5)(3x+5)=0 equation:

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

We multiply parentheses ..

(+6x^2+10x-15x-25)=0

We get rid of parentheses

6x^2+10x-15x-25=0

We add all the numbers together, and all the variables

6x^2-5x-25=0

a = 6; b = -5; c = -25;
Δ = b2-4ac
Δ = -52-4·6·(-25)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-25}{2*6}=\frac{-20}{12}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+25}{2*6}=\frac{30}{12}
=2+1/2
$