10x^2-78x+80=0

Solution for 10x^2-78x+80=0 equation:

10x^2-78x+80=0

a = 10; b = -78; c = +80;
Δ = b2-4ac
Δ = -782-4·10·80
Δ = 2884
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:

$\sqrt{\Delta}=\sqrt{2884}=\sqrt{4*721}=\sqrt{4}*\sqrt{721}=2\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{721}}{2*10}=\frac{78-2\sqrt{721}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{721}}{2*10}=\frac{78+2\sqrt{721}}{20}
$