10x(x+10)-7=13

Solution for 10x(x+10)-7=13 equation:

10x(x+10)-7=13

We move all terms to the left:

10x(x+10)-7-(13)=0

We add all the numbers together, and all the variables

10x(x+10)-20=0

We multiply parentheses

10x^2+100x-20=0

a = 10; b = 100; c = -20;
Δ = b2-4ac
Δ = 1002-4·10·(-20)
Δ = 10800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-60\sqrt{3}}{2*10}=\frac{-100-60\sqrt{3}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+60\sqrt{3}}{2*10}=\frac{-100+60\sqrt{3}}{20}
$