x^2+9=7x

Solution for x^2+9=7x equation:

x^2+9=7x

We move all terms to the left:

x^2+9-(7x)=0

a = 1; b = -7; c = +9;
Δ = b2-4ac
Δ = -72-4·1·9
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{13}}{2*1}=\frac{7-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{13}}{2*1}=\frac{7+\sqrt{13}}{2}
$