x^2+5x+1=2x^2-9

Solution for x^2+5x+1=2x^2-9 equation:

x^2+5x+1=2x^2-9

We move all terms to the left:

x^2+5x+1-(2x^2-9)=0

We get rid of parentheses

x^2-2x^2+5x+9+1=0

We add all the numbers together, and all the variables

-1x^2+5x+10=0

a = -1; b = 5; c = +10;
Δ = b2-4ac
Δ = 52-4·(-1)·10
Δ = 65
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{-(5)-\sqrt{65}}{2*-1}=\frac{-5-\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*-1}=\frac{-5+\sqrt{65}}{-2}
$