(4x+5)(5x-6)=0

Solution for (4x+5)(5x-6)=0 equation:

(4x+5)(5x-6)=0

We multiply parentheses ..

(+20x^2-24x+25x-30)=0

We get rid of parentheses

20x^2-24x+25x-30=0

We add all the numbers together, and all the variables

20x^2+x-30=0

a = 20; b = 1; c = -30;
Δ = b2-4ac
Δ = 12-4·20·(-30)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-49}{2*20}=\frac{-50}{40}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+49}{2*20}=\frac{48}{40}
=1+1/5
$