3x+8=x2-7

Solution for 3x+8=x2-7 equation:

3x+8=x2-7

We move all terms to the left:

3x+8-(x2-7)=0

We add all the numbers together, and all the variables

-(+x^2-7)+3x+8=0

We get rid of parentheses

-x^2+3x+7+8=0

We add all the numbers together, and all the variables

-1x^2+3x+15=0

a = -1; b = 3; c = +15;
Δ = b2-4ac
Δ = 32-4·(-1)·15
Δ = 69
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{-(3)-\sqrt{69}}{2*-1}=\frac{-3-\sqrt{69}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{69}}{2*-1}=\frac{-3+\sqrt{69}}{-2}
$