5x^2+100x=1500

Solution for 5x^2+100x=1500 equation:

5x^2+100x=1500

We move all terms to the left:

5x^2+100x-(1500)=0

a = 5; b = 100; c = -1500;
Δ = b2-4ac
Δ = 1002-4·5·(-1500)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-200}{2*5}=\frac{-300}{10}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+200}{2*5}=\frac{100}{10}
=10
$