(5x-9)(2x+6)=0

Solution for (5x-9)(2x+6)=0 equation:

(5x-9)(2x+6)=0

We multiply parentheses ..

(+10x^2+30x-18x-54)=0

We get rid of parentheses

10x^2+30x-18x-54=0

We add all the numbers together, and all the variables

10x^2+12x-54=0

a = 10; b = 12; c = -54;
Δ = b2-4ac
Δ = 122-4·10·(-54)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-48}{2*10}=\frac{-60}{20}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+48}{2*10}=\frac{36}{20}
=1+4/5
$