4x2=59x+80

Solution for 4x2=59x+80 equation:

4x^2=59x+80

We move all terms to the left:

4x^2-(59x+80)=0

We get rid of parentheses

4x^2-59x-80=0

a = 4; b = -59; c = -80;
Δ = b2-4ac
Δ = -592-4·4·(-80)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-69}{2*4}=\frac{-10}{8}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+69}{2*4}=\frac{128}{8}
=16
$