4x^2-33=13x

Solution for 4x^2-33=13x equation:

4x^2-33=13x

We move all terms to the left:

4x^2-33-(13x)=0

a = 4; b = -13; c = -33;
Δ = b2-4ac
Δ = -132-4·4·(-33)
Δ = 697
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{-(-13)-\sqrt{697}}{2*4}=\frac{13-\sqrt{697}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{697}}{2*4}=\frac{13+\sqrt{697}}{8}
$