2x^2-9=-x^2+8x-5

Solution for 2x^2-9=-x^2+8x-5 equation:

2x^2-9=-x^2+8x-5

We move all terms to the left:

2x^2-9-(-x^2+8x-5)=0

We get rid of parentheses

2x^2+x^2-8x+5-9=0

We add all the numbers together, and all the variables

3x^2-8x-4=0

a = 3; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·3·(-4)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*3}=\frac{8-4\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*3}=\frac{8+4\sqrt{7}}{6}
$