(x-9)(x+9)=10(-x-10.2)

Solution for (x-9)(x+9)=10(-x-10.2) equation:

(x-9)(x+9)=10(-x-10.2)

We move all terms to the left:

(x-9)(x+9)-(10(-x-10.2))=0

We add all the numbers together, and all the variables

(x-9)(x+9)-(10(-1x-10.2))=0

We use the square of the difference formula

x^2-(10(-1x-10.2))-81=0


We calculate terms in parentheses: -(10(-1x-10.2)), so:

10(-1x-10.2)

We multiply parentheses

-10x-102

Back to the equation:

-(-10x-102)


We get rid of parentheses

x^2+10x+102-81=0

We add all the numbers together, and all the variables

x^2+10x+21=0

a = 1; b = 10; c = +21;
Δ = b2-4ac
Δ = 102-4·1·21
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*1}=\frac{-6}{2}
=-3
$