5x^2=40x+5

Solution for 5x^2=40x+5 equation:

5x^2=40x+5

We move all terms to the left:

5x^2-(40x+5)=0

We get rid of parentheses

5x^2-40x-5=0

a = 5; b = -40; c = -5;
Δ = b2-4ac
Δ = -402-4·5·(-5)
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{17}}{2*5}=\frac{40-10\sqrt{17}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{17}}{2*5}=\frac{40+10\sqrt{17}}{10}
$