(5x-8)(3x+27)=0

Solution for (5x-8)(3x+27)=0 equation:

(5x-8)(3x+27)=0

We multiply parentheses ..

(+15x^2+135x-24x-216)=0

We get rid of parentheses

15x^2+135x-24x-216=0

We add all the numbers together, and all the variables

15x^2+111x-216=0

a = 15; b = 111; c = -216;
Δ = b2-4ac
Δ = 1112-4·15·(-216)
Δ = 25281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25281}=159$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-159}{2*15}=\frac{-270}{30}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+159}{2*15}=\frac{48}{30}
=1+3/5
$