3q^2-10q=77

Solution for 3q^2-10q=77 equation:

3q^2-10q=77

We move all terms to the left:

3q^2-10q-(77)=0

a = 3; b = -10; c = -77;
Δ = b2-4ac
Δ = -102-4·3·(-77)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-32}{2*3}=\frac{-22}{6}
=-3+2/3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+32}{2*3}=\frac{42}{6}
=7
$