6(x+1)-10=4(x-1)2x

Solution for 6(x+1)-10=4(x-1)2x equation:

6(x+1)-10=4(x-1)2x

We move all terms to the left:

6(x+1)-10-(4(x-1)2x)=0

We multiply parentheses

6x-(4(x-1)2x)+6-10=0


We calculate terms in parentheses: -(4(x-1)2x), so:

4(x-1)2x

We multiply parentheses

8x^2-8x

Back to the equation:

-(8x^2-8x)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-8x^2+6x+8x-4=0

We add all the numbers together, and all the variables

-8x^2+14x-4=0

a = -8; b = 14; c = -4;
Δ = b2-4ac
Δ = 142-4·(-8)·(-4)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{17}}{2*-8}=\frac{-14-2\sqrt{17}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{17}}{2*-8}=\frac{-14+2\sqrt{17}}{-16}
$