4x^2-7x+12=6x+9

Solution for 4x^2-7x+12=6x+9 equation:

4x^2-7x+12=6x+9

We move all terms to the left:

4x^2-7x+12-(6x+9)=0

We get rid of parentheses

4x^2-7x-6x-9+12=0

We add all the numbers together, and all the variables

4x^2-13x+3=0

a = 4; b = -13; c = +3;
Δ = b2-4ac
Δ = -132-4·4·3
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-11}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+11}{2*4}=\frac{24}{8}
=3
$