x=2x^2+9x+5

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

x=2x^2+9x+5

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-8x-5=0

a = -2; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·(-2)·(-5)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{6}}{2*-2}=\frac{8-2\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{6}}{2*-2}=\frac{8+2\sqrt{6}}{-4}
$