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

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

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

We multiply parentheses ..

(+7x^2-42x+5x-30)=0

We get rid of parentheses

7x^2-42x+5x-30=0

We add all the numbers together, and all the variables

7x^2-37x-30=0

a = 7; b = -37; c = -30;
Δ = b2-4ac
Δ = -372-4·7·(-30)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-47}{2*7}=\frac{-10}{14}
=-5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+47}{2*7}=\frac{84}{14}
=6
$