28-(3x+4)=2x(x+6)+x

Solution for 28-(3x+4)=2x(x+6)+x equation:

28-(3x+4)=2x(x+6)+x

We move all terms to the left:

28-(3x+4)-(2x(x+6)+x)=0

We get rid of parentheses

-3x-(2x(x+6)+x)-4+28=0


We calculate terms in parentheses: -(2x(x+6)+x), so:

2x(x+6)+x

We add all the numbers together, and all the variables

x+2x(x+6)

We multiply parentheses

2x^2+x+12x

We add all the numbers together, and all the variables

2x^2+13x

Back to the equation:

-(2x^2+13x)


We add all the numbers together, and all the variables

-3x-(2x^2+13x)+24=0

We get rid of parentheses

-2x^2-3x-13x+24=0

We add all the numbers together, and all the variables

-2x^2-16x+24=0

a = -2; b = -16; c = +24;
Δ = b2-4ac
Δ = -162-4·(-2)·24
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{7}}{2*-2}=\frac{16-8\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{7}}{2*-2}=\frac{16+8\sqrt{7}}{-4}
$