9x+8=x2+14

Solution for 9x+8=x2+14 equation:

9x+8=x2+14

We move all terms to the left:

9x+8-(x2+14)=0

We add all the numbers together, and all the variables

-(+x^2+14)+9x+8=0

We get rid of parentheses

-x^2+9x-14+8=0

We add all the numbers together, and all the variables

-1x^2+9x-6=0

a = -1; b = 9; c = -6;
Δ = b2-4ac
Δ = 92-4·(-1)·(-6)
Δ = 57
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{-(9)-\sqrt{57}}{2*-1}=\frac{-9-\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{57}}{2*-1}=\frac{-9+\sqrt{57}}{-2}
$