10q^2+15q=100

Solution for 10q^2+15q=100 equation:

10q^2+15q=100

We move all terms to the left:

10q^2+15q-(100)=0

a = 10; b = 15; c = -100;
Δ = b2-4ac
Δ = 152-4·10·(-100)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-65}{2*10}=\frac{-80}{20}
=-4
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+65}{2*10}=\frac{50}{20}
=2+1/2
$