5x^2-52x+64=0

Solution for 5x^2-52x+64=0 equation:

5x^2-52x+64=0

a = 5; b = -52; c = +64;
Δ = b2-4ac
Δ = -522-4·5·64
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{89}}{2*5}=\frac{52-4\sqrt{89}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{89}}{2*5}=\frac{52+4\sqrt{89}}{10}
$