3x+12+4x^2-3=7x+9

Solution for 3x+12+4x^2-3=7x+9 equation:

3x+12+4x^2-3=7x+9

We move all terms to the left:

3x+12+4x^2-3-(7x+9)=0

We add all the numbers together, and all the variables

4x^2+3x-(7x+9)+9=0

We get rid of parentheses

4x^2+3x-7x-9+9=0

We add all the numbers together, and all the variables

4x^2-4x=0

a = 4; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·4·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*4}=\frac{8}{8}
=1
$