33x+7x^2=10

Solution for 33x+7x^2=10 equation:

33x+7x^2=10

We move all terms to the left:

33x+7x^2-(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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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