x(x+10)+7(x+10)=0

Solution for x(x+10)+7(x+10)=0 equation:

x(x+10)+7(x+10)=0

We multiply parentheses

x^2+10x+7x+70=0

We add all the numbers together, and all the variables

x^2+17x+70=0

a = 1; b = 17; c = +70;
Δ = b2-4ac
Δ = 172-4·1·70
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3}{2*1}=\frac{-14}{2}
=-7
$