X^2=5-9x

Solution for X^2=5-9x equation:

X^2=5-9X

We move all terms to the left:

X^2-(5-9X)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

X^2+9X-5=0

a = 1; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·1·(-5)
Δ = 101
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{-(9)-\sqrt{101}}{2*1}=\frac{-9-\sqrt{101}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{101}}{2*1}=\frac{-9+\sqrt{101}}{2}
$