x+3=2x^2-19+5

Solution for x+3=2x^2-19+5 equation:

x+3=2x^2-19+5

We move all terms to the left:

x+3-(2x^2-19+5)=0

We get rid of parentheses

-2x^2+x+19-5+3=0

We add all the numbers together, and all the variables

-2x^2+x+17=0

a = -2; b = 1; c = +17;
Δ = b2-4ac
Δ = 12-4·(-2)·17
Δ = 137
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{-(1)-\sqrt{137}}{2*-2}=\frac{-1-\sqrt{137}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{137}}{2*-2}=\frac{-1+\sqrt{137}}{-4}
$