4x^2-136x=480

Solution for 4x^2-136x=480 equation:

4x^2-136x=480

We move all terms to the left:

4x^2-136x-(480)=0

a = 4; b = -136; c = -480;
Δ = b2-4ac
Δ = -1362-4·4·(-480)
Δ = 26176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{26176}=\sqrt{64*409}=\sqrt{64}*\sqrt{409}=8\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-8\sqrt{409}}{2*4}=\frac{136-8\sqrt{409}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+8\sqrt{409}}{2*4}=\frac{136+8\sqrt{409}}{8}
$