5x^2-100x=-405

Solution for 5x^2-100x=-405 equation:

5x^2-100x=-405

We move all terms to the left:

5x^2-100x-(-405)=0

We add all the numbers together, and all the variables

5x^2-100x+405=0

a = 5; b = -100; c = +405;
Δ = b2-4ac
Δ = -1002-4·5·405
Δ = 1900
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:

$\sqrt{\Delta}=\sqrt{1900}=\sqrt{100*19}=\sqrt{100}*\sqrt{19}=10\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-10\sqrt{19}}{2*5}=\frac{100-10\sqrt{19}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+10\sqrt{19}}{2*5}=\frac{100+10\sqrt{19}}{10}
$