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

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

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

We multiply parentheses

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

We add all the numbers together, and all the variables

5x^2+23x-42=0

a = 5; b = 23; c = -42;
Δ = b2-4ac
Δ = 232-4·5·(-42)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-37}{2*5}=\frac{-60}{10}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+37}{2*5}=\frac{14}{10}
=1+2/5
$