x^2+3x=100

Solution for x^2+3x=100 equation:

x^2+3x=100

We move all terms to the left:

x^2+3x-(100)=0

a = 1; b = 3; c = -100;
Δ = b2-4ac
Δ = 32-4·1·(-100)
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{409}}{2*1}=\frac{-3-\sqrt{409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{409}}{2*1}=\frac{-3+\sqrt{409}}{2}
$