5x^2=40x-6

Solution for 5x^2=40x-6 equation:

5x^2=40x-6

We move all terms to the left:

5x^2-(40x-6)=0

We get rid of parentheses

5x^2-40x+6=0

a = 5; b = -40; c = +6;
Δ = b2-4ac
Δ = -402-4·5·6
Δ = 1480
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:

$\sqrt{\Delta}=\sqrt{1480}=\sqrt{4*370}=\sqrt{4}*\sqrt{370}=2\sqrt{370}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{370}}{2*5}=\frac{40-2\sqrt{370}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{370}}{2*5}=\frac{40+2\sqrt{370}}{10}
$