49q^2-14q=15

Solution for 49q^2-14q=15 equation:

49q^2-14q=15

We move all terms to the left:

49q^2-14q-(15)=0

a = 49; b = -14; c = -15;
Δ = b2-4ac
Δ = -142-4·49·(-15)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-56}{2*49}=\frac{-42}{98}
=-3/7
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+56}{2*49}=\frac{70}{98}
=5/7
$