5x+x2=100

Solution for 5x+x2=100 equation:

5x+x2=100

We move all terms to the left:

5x+x2-(100)=0

We add all the numbers together, and all the variables

x^2+5x-100=0

a = 1; b = 5; c = -100;
Δ = b2-4ac
Δ = 52-4·1·(-100)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{17}}{2*1}=\frac{-5-5\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{17}}{2*1}=\frac{-5+5\sqrt{17}}{2}
$