8x2+36x+30=10-x2

Solution for 8x2+36x+30=10-x2 equation:

8x^2+36x+30=10-x2

We move all terms to the left:

8x^2+36x+30-(10-x2)=0

We add all the numbers together, and all the variables

8x^2-(-1x^2+10)+36x+30=0

We get rid of parentheses

8x^2+1x^2+36x-10+30=0

We add all the numbers together, and all the variables

9x^2+36x+20=0

a = 9; b = 36; c = +20;
Δ = b2-4ac
Δ = 362-4·9·20
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-24}{2*9}=\frac{-60}{18}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+24}{2*9}=\frac{-12}{18}
=-2/3
$