2(x+5)=6(x-1)x=4

Solution for 2(x+5)=6(x-1)x=4 equation:

2(x+5)=6(x-1)x=4

We move all terms to the left:

2(x+5)-(6(x-1)x)=0

We multiply parentheses

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


We calculate terms in parentheses: -(6(x-1)x), so:

6(x-1)x

We multiply parentheses

6x^2-6x

Back to the equation:

-(6x^2-6x)


We get rid of parentheses

-6x^2+2x+6x+10=0

We add all the numbers together, and all the variables

-6x^2+8x+10=0

a = -6; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-6)·10
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{19}}{2*-6}=\frac{-8-4\sqrt{19}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{19}}{2*-6}=\frac{-8+4\sqrt{19}}{-12}
$