(3x+7)(5x-6)=0

Solution for (3x+7)(5x-6)=0 equation:

(3x+7)(5x-6)=0

We multiply parentheses ..

(+15x^2-18x+35x-42)=0

We get rid of parentheses

15x^2-18x+35x-42=0

We add all the numbers together, and all the variables

15x^2+17x-42=0

a = 15; b = 17; c = -42;
Δ = b2-4ac
Δ = 172-4·15·(-42)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-53}{2*15}=\frac{-70}{30}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+53}{2*15}=\frac{36}{30}
=1+1/5
$