2x^2+13x-73=x^2-19

Solution for 2x^2+13x-73=x^2-19 equation:

2x^2+13x-73=x^2-19

We move all terms to the left:

2x^2+13x-73-(x^2-19)=0

We get rid of parentheses

2x^2-x^2+13x+19-73=0

We add all the numbers together, and all the variables

x^2+13x-54=0

a = 1; b = 13; c = -54;
Δ = b2-4ac
Δ = 132-4·1·(-54)
Δ = 385
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{-(13)-\sqrt{385}}{2*1}=\frac{-13-\sqrt{385}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{385}}{2*1}=\frac{-13+\sqrt{385}}{2}
$