7n^2-33n=10

Solution for 7n^2-33n=10 equation:

7n^2-33n=10

We move all terms to the left:

7n^2-33n-(10)=0

a = 7; b = -33; c = -10;
Δ = b2-4ac
Δ = -332-4·7·(-10)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-37}{2*7}=\frac{-4}{14}
=-2/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+37}{2*7}=\frac{70}{14}
=5
$