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

Solution for 2x^2+9x=x^2-14 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^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
$