(5x-6)(2x+5)=0

Solution for (5x-6)(2x+5)=0 equation:

(5x-6)(2x+5)=0

We multiply parentheses ..

(+10x^2+25x-12x-30)=0

We get rid of parentheses

10x^2+25x-12x-30=0

We add all the numbers together, and all the variables

10x^2+13x-30=0

a = 10; b = 13; c = -30;
Δ = b2-4ac
Δ = 132-4·10·(-30)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-37}{2*10}=\frac{-50}{20}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+37}{2*10}=\frac{24}{20}
=1+1/5
$