14x+4(2x-6)=x(2x+8)

Solution for 14x+4(2x-6)=x(2x+8) equation:

14x+4(2x-6)=x(2x+8)

We move all terms to the left:

14x+4(2x-6)-(x(2x+8))=0

We multiply parentheses

14x+8x-(x(2x+8))-24=0


We calculate terms in parentheses: -(x(2x+8)), so:

x(2x+8)

We multiply parentheses

2x^2+8x

Back to the equation:

-(2x^2+8x)


We add all the numbers together, and all the variables

22x-(2x^2+8x)-24=0

We get rid of parentheses

-2x^2+22x-8x-24=0

We add all the numbers together, and all the variables

-2x^2+14x-24=0

a = -2; b = 14; c = -24;
Δ = b2-4ac
Δ = 142-4·(-2)·(-24)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*-2}=\frac{-12}{-4}
=+3
$