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

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

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

We multiply parentheses

x^2+6x^2+5x+30x-7x-35=0

We add all the numbers together, and all the variables

7x^2+28x-35=0

a = 7; b = 28; c = -35;
Δ = b2-4ac
Δ = 282-4·7·(-35)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-42}{2*7}=\frac{-70}{14}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+42}{2*7}=\frac{14}{14}
=1
$