(x+9)(x-9)=-5x

Solution for (x+9)(x-9)=-5x equation:

(x+9)(x-9)=-5x

We move all terms to the left:

(x+9)(x-9)-(-5x)=0

We use the square of the difference formula

x^2-(-5x)-81=0

We get rid of parentheses

x^2+5x-81=0

a = 1; b = 5; c = -81;
Δ = b2-4ac
Δ = 52-4·1·(-81)
Δ = 349
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{-(5)-\sqrt{349}}{2*1}=\frac{-5-\sqrt{349}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{349}}{2*1}=\frac{-5+\sqrt{349}}{2}
$