5x(x+8)=-7

Solution for 5x(x+8)=-7 equation:

5x(x+8)=-7

We move all terms to the left:

5x(x+8)-(-7)=0

We add all the numbers together, and all the variables

5x(x+8)+7=0

We multiply parentheses

5x^2+40x+7=0

a = 5; b = 40; c = +7;
Δ = b2-4ac
Δ = 402-4·5·7
Δ = 1460
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:

$\sqrt{\Delta}=\sqrt{1460}=\sqrt{4*365}=\sqrt{4}*\sqrt{365}=2\sqrt{365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{365}}{2*5}=\frac{-40-2\sqrt{365}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{365}}{2*5}=\frac{-40+2\sqrt{365}}{10}
$