a^2-6a=25

Solution for a^2-6a=25 equation:

a^2-6a=25

We move all terms to the left:

a^2-6a-(25)=0

a = 1; b = -6; c = -25;
Δ = b2-4ac
Δ = -62-4·1·(-25)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{34}}{2*1}=\frac{6-2\sqrt{34}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{34}}{2*1}=\frac{6+2\sqrt{34}}{2}
$