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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+13x-15=0

a = 6; b = 13; c = -15;
Δ = b2-4ac
Δ = 132-4·6·(-15)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-23}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+23}{2*6}=\frac{10}{12}
=5/6
$