2x^2+5x+8=-x^2+7

Solution for 2x^2+5x+8=-x^2+7 equation:

2x^2+5x+8=-x^2+7

We move all terms to the left:

2x^2+5x+8-(-x^2+7)=0

We get rid of parentheses

2x^2+x^2+5x-7+8=0

We add all the numbers together, and all the variables

3x^2+5x+1=0

a = 3; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·3·1
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{13}}{2*3}=\frac{-5-\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{13}}{2*3}=\frac{-5+\sqrt{13}}{6}
$