7=-x^2+9x

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

7=-x^2+9x

We move all terms to the left:

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

We get rid of parentheses

x^2-9x+7=0

a = 1; b = -9; c = +7;
Δ = b2-4ac
Δ = -92-4·1·7
Δ = 53
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{-(-9)-\sqrt{53}}{2*1}=\frac{9-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{53}}{2*1}=\frac{9+\sqrt{53}}{2}
$