9x=x2+14

Solution for 9x=x2+14 equation:

9x=x2+14

We move all terms to the left:

9x-(x2+14)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+9x-14=0

We add all the numbers together, and all the variables

-1x^2+9x-14=0

a = -1; b = 9; c = -14;
Δ = b2-4ac
Δ = 92-4·(-1)·(-14)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5}{2*-1}=\frac{-4}{-2}
=+2
$