x=9x^2-6+5

Solution for x=9x^2-6+5 equation:

x=9x^2-6+5

We move all terms to the left:

x-(9x^2-6+5)=0

We get rid of parentheses

-9x^2+x+6-5=0

We add all the numbers together, and all the variables

-9x^2+x+1=0

a = -9; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-9)·1
Δ = 37
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{37}}{2*-9}=\frac{-1-\sqrt{37}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*-9}=\frac{-1+\sqrt{37}}{-18}
$