2q^2-31q+15=0

Solution for 2q^2-31q+15=0 equation:

2q^2-31q+15=0

a = 2; b = -31; c = +15;
Δ = b2-4ac
Δ = -312-4·2·15
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-29}{2*2}=\frac{2}{4}
=1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+29}{2*2}=\frac{60}{4}
=15
$