5a^2-15a+5=0

Solution for 5a^2-15a+5=0 equation:

5a^2-15a+5=0

a = 5; b = -15; c = +5;
Δ = b2-4ac
Δ = -152-4·5·5
Δ = 125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{5}}{2*5}=\frac{15-5\sqrt{5}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{5}}{2*5}=\frac{15+5\sqrt{5}}{10}
$