5x(x+8)=35

Solution for 5x(x+8)=35 equation:

5x(x+8)=35

We move all terms to the left:

5x(x+8)-(35)=0

We multiply parentheses

5x^2+40x-35=0

a = 5; b = 40; c = -35;
Δ = b2-4ac
Δ = 402-4·5·(-35)
Δ = 2300
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:

$\sqrt{\Delta}=\sqrt{2300}=\sqrt{100*23}=\sqrt{100}*\sqrt{23}=10\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{23}}{2*5}=\frac{-40-10\sqrt{23}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{23}}{2*5}=\frac{-40+10\sqrt{23}}{10}
$