5x^2-40x=-38

Solution for 5x^2-40x=-38 equation:

5x^2-40x=-38

We move all terms to the left:

5x^2-40x-(-38)=0

We add all the numbers together, and all the variables

5x^2-40x+38=0

a = 5; b = -40; c = +38;
Δ = b2-4ac
Δ = -402-4·5·38
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{210}}{2*5}=\frac{40-2\sqrt{210}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{210}}{2*5}=\frac{40+2\sqrt{210}}{10}
$