5u^2-76u+179=0

Solution for 5u^2-76u+179=0 equation:

5u^2-76u+179=0

a = 5; b = -76; c = +179;
Δ = b2-4ac
Δ = -762-4·5·179
Δ = 2196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-6\sqrt{61}}{2*5}=\frac{76-6\sqrt{61}}{10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+6\sqrt{61}}{2*5}=\frac{76+6\sqrt{61}}{10}
$