7x^2+33x=8000

Solution for 7x^2+33x=8000 equation:

7x^2+33x=8000

We move all terms to the left:

7x^2+33x-(8000)=0

a = 7; b = 33; c = -8000;
Δ = b2-4ac
Δ = 332-4·7·(-8000)
Δ = 225089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{225089}}{2*7}=\frac{-33-\sqrt{225089}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{225089}}{2*7}=\frac{-33+\sqrt{225089}}{14}
$