5x^2-25x+10=100

Solution for 5x^2-25x+10=100 equation:

5x^2-25x+10=100

We move all terms to the left:

5x^2-25x+10-(100)=0

We add all the numbers together, and all the variables

5x^2-25x-90=0

a = 5; b = -25; c = -90;
Δ = b2-4ac
Δ = -252-4·5·(-90)
Δ = 2425
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:

$\sqrt{\Delta}=\sqrt{2425}=\sqrt{25*97}=\sqrt{25}*\sqrt{97}=5\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{97}}{2*5}=\frac{25-5\sqrt{97}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{97}}{2*5}=\frac{25+5\sqrt{97}}{10}
$