3x^2-4x=28+x^2

Solution for 3x^2-4x=28+x^2 equation:

3x^2-4x=28+x^2

We move all terms to the left:

3x^2-4x-(28+x^2)=0

We get rid of parentheses

3x^2-x^2-4x-28=0

We add all the numbers together, and all the variables

2x^2-4x-28=0

a = 2; b = -4; c = -28;
Δ = b2-4ac
Δ = -42-4·2·(-28)
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{15}}{2*2}=\frac{4-4\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{15}}{2*2}=\frac{4+4\sqrt{15}}{4}
$