7q^2-19q=23

Solution for 7q^2-19q=23 equation:

7q^2-19q=23

We move all terms to the left:

7q^2-19q-(23)=0

a = 7; b = -19; c = -23;
Δ = b2-4ac
Δ = -192-4·7·(-23)
Δ = 1005
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{1005}}{2*7}=\frac{19-\sqrt{1005}}{14}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1005}}{2*7}=\frac{19+\sqrt{1005}}{14}
$