4x^2-20=59x

Solution for 4x^2-20=59x equation:

4x^2-20=59x

We move all terms to the left:

4x^2-20-(59x)=0

a = 4; b = -59; c = -20;
Δ = b2-4ac
Δ = -592-4·4·(-20)
Δ = 3801
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{-(-59)-\sqrt{3801}}{2*4}=\frac{59-\sqrt{3801}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{3801}}{2*4}=\frac{59+\sqrt{3801}}{8}
$