4x2=40x+64

Solution for 4x2=40x+64 equation:

4x^2=40x+64

We move all terms to the left:

4x^2-(40x+64)=0

We get rid of parentheses

4x^2-40x-64=0

a = 4; b = -40; c = -64;
Δ = b2-4ac
Δ = -402-4·4·(-64)
Δ = 2624
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:

$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{41}}{2*4}=\frac{40-8\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{41}}{2*4}=\frac{40+8\sqrt{41}}{8}
$