4x^2-24=29x

Solution for 4x^2-24=29x equation:

4x^2-24=29x

We move all terms to the left:

4x^2-24-(29x)=0

a = 4; b = -29; c = -24;
Δ = b2-4ac
Δ = -292-4·4·(-24)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-35}{2*4}=\frac{-6}{8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+35}{2*4}=\frac{64}{8}
=8
$