9x^2+4x-16=-x^2

Solution for 9x^2+4x-16=-x^2 equation:

9x^2+4x-16=-x^2

We move all terms to the left:

9x^2+4x-16-(-x^2)=0

We get rid of parentheses

9x^2+x^2+4x-16=0

We add all the numbers together, and all the variables

10x^2+4x-16=0

a = 10; b = 4; c = -16;
Δ = b2-4ac
Δ = 42-4·10·(-16)
Δ = 656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{41}}{2*10}=\frac{-4-4\sqrt{41}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{41}}{2*10}=\frac{-4+4\sqrt{41}}{20}
$