X^2+7+2=9x+5

Solution for X^2+7+2=9x+5 equation:

X^2+7+2=9X+5

We move all terms to the left:

X^2+7+2-(9X+5)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2-9X+4=0

a = 1; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·1·4
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{-(-9)-\sqrt{65}}{2*1}=\frac{9-\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{65}}{2*1}=\frac{9+\sqrt{65}}{2}
$