X^2-9x-8=10-x^2

Solution for X^2-9x-8=10-x^2 equation:

X^2-9X-8=10-X^2

We move all terms to the left:

X^2-9X-8-(10-X^2)=0

We get rid of parentheses

X^2+X^2-9X-10-8=0

We add all the numbers together, and all the variables

2X^2-9X-18=0

a = 2; b = -9; c = -18;
Δ = b2-4ac
Δ = -92-4·2·(-18)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*2}=\frac{-6}{4}
=-1+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*2}=\frac{24}{4}
=6
$