2x^2+15x+38=x^2

Solution for 2x^2+15x+38=x^2 equation:

2x^2+15x+38=x^2

We move all terms to the left:

2x^2+15x+38-(x^2)=0

determiningTheFunctionDomain
2x^2-x^2+15x+38=0

We add all the numbers together, and all the variables

x^2+15x+38=0

a = 1; b = 15; c = +38;
Δ = b2-4ac
Δ = 152-4·1·38
Δ = 73
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{-(15)-\sqrt{73}}{2*1}=\frac{-15-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{73}}{2*1}=\frac{-15+\sqrt{73}}{2}
$