5q^2-14q=15

Solution for 5q^2-14q=15 equation:

5q^2-14q=15

We move all terms to the left:

5q^2-14q-(15)=0

a = 5; b = -14; c = -15;
Δ = b2-4ac
Δ = -142-4·5·(-15)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{31}}{2*5}=\frac{14-4\sqrt{31}}{10}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{31}}{2*5}=\frac{14+4\sqrt{31}}{10}
$