3q^2-4q+10=94

Solution for 3q^2-4q+10=94 equation:

3q^2-4q+10=94

We move all terms to the left:

3q^2-4q+10-(94)=0

We add all the numbers together, and all the variables

3q^2-4q-84=0

a = 3; b = -4; c = -84;
Δ = b2-4ac
Δ = -42-4·3·(-84)
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{-(-4)-32}{2*3}=\frac{-28}{6}
=-4+2/3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+32}{2*3}=\frac{36}{6}
=6
$