a^2=10a-7

Solution for a^2=10a-7 equation:

a^2=10a-7

We move all terms to the left:

a^2-(10a-7)=0

We get rid of parentheses

a^2-10a+7=0

a = 1; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·1·7
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{2}}{2*1}=\frac{10-6\sqrt{2}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{2}}{2*1}=\frac{10+6\sqrt{2}}{2}
$