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

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

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

We multiply parentheses ..

(+30x^2-35x+36x-42)=0

We get rid of parentheses

30x^2-35x+36x-42=0

We add all the numbers together, and all the variables

30x^2+x-42=0

a = 30; b = 1; c = -42;
Δ = b2-4ac
Δ = 12-4·30·(-42)
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-71}{2*30}=\frac{-72}{60}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+71}{2*30}=\frac{70}{60}
=1+1/6
$