6+8x(x-1)=2(3x+4)

Solution for 6+8x(x-1)=2(3x+4) equation:

6+8x(x-1)=2(3x+4)

We move all terms to the left:

6+8x(x-1)-(2(3x+4))=0

We multiply parentheses

8x^2-8x-(2(3x+4))+6=0


We calculate terms in parentheses: -(2(3x+4)), so:

2(3x+4)

We multiply parentheses

6x+8

Back to the equation:

-(6x+8)


We get rid of parentheses

8x^2-8x-6x-8+6=0

We add all the numbers together, and all the variables

8x^2-14x-2=0

a = 8; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·8·(-2)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{65}}{2*8}=\frac{14-2\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{65}}{2*8}=\frac{14+2\sqrt{65}}{16}
$