4x^2-3x+9=4x+6

Solution for 4x^2-3x+9=4x+6 equation:

4x^2-3x+9=4x+6

We move all terms to the left:

4x^2-3x+9-(4x+6)=0

We get rid of parentheses

4x^2-3x-4x-6+9=0

We add all the numbers together, and all the variables

4x^2-7x+3=0

a = 4; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·4·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*4}=\frac{6}{8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*4}=\frac{8}{8}
=1
$