x^2-76x+78=0

Solution for x^2-76x+78=0 equation:

x^2-76x+78=0

a = 1; b = -76; c = +78;
Δ = b2-4ac
Δ = -762-4·1·78
Δ = 5464
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:

$\sqrt{\Delta}=\sqrt{5464}=\sqrt{4*1366}=\sqrt{4}*\sqrt{1366}=2\sqrt{1366}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-2\sqrt{1366}}{2*1}=\frac{76-2\sqrt{1366}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+2\sqrt{1366}}{2*1}=\frac{76+2\sqrt{1366}}{2}
$