(5x+6)(6x-18)=0

Solution for (5x+6)(6x-18)=0 equation:

(5x+6)(6x-18)=0

We multiply parentheses ..

(+30x^2-90x+36x-108)=0

We get rid of parentheses

30x^2-90x+36x-108=0

We add all the numbers together, and all the variables

30x^2-54x-108=0

a = 30; b = -54; c = -108;
Δ = b2-4ac
Δ = -542-4·30·(-108)
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-126}{2*30}=\frac{-72}{60}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+126}{2*30}=\frac{180}{60}
=3
$