a^2-30a+75=0

Solution for a^2-30a+75=0 equation:

a^2-30a+75=0

a = 1; b = -30; c = +75;
Δ = b2-4ac
Δ = -302-4·1·75
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{6}}{2*1}=\frac{30-10\sqrt{6}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{6}}{2*1}=\frac{30+10\sqrt{6}}{2}
$