(2x+3)(5x-6)=0

Solution for (2x+3)(5x-6)=0 equation:

(2x+3)(5x-6)=0

We multiply parentheses ..

(+10x^2-12x+15x-18)=0

We get rid of parentheses

10x^2-12x+15x-18=0

We add all the numbers together, and all the variables

10x^2+3x-18=0

a = 10; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·10·(-18)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*10}=\frac{-30}{20}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*10}=\frac{24}{20}
=1+1/5
$