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

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

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

We multiply parentheses ..

(+5x^2+15x-6x-18)=0

We get rid of parentheses

5x^2+15x-6x-18=0

We add all the numbers together, and all the variables

5x^2+9x-18=0

a = 5; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·5·(-18)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*5}=\frac{12}{10}
=1+1/5
$