4-12x+9x^2=5x+6

Solution for 4-12x+9x^2=5x+6 equation:

4-12x+9x^2=5x+6

We move all terms to the left:

4-12x+9x^2-(5x+6)=0

We get rid of parentheses

9x^2-12x-5x-6+4=0

We add all the numbers together, and all the variables

9x^2-17x-2=0

a = 9; b = -17; c = -2;
Δ = b2-4ac
Δ = -172-4·9·(-2)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-19}{2*9}=\frac{-2}{18}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+19}{2*9}=\frac{36}{18}
=2
$