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

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

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

We move all terms to the left:

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

We multiply parentheses

4x-(6(x-1)x)+12=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+4x+6x+12=0

We add all the numbers together, and all the variables

-6x^2+10x+12=0

a = -6; b = 10; c = +12;
Δ = b2-4ac
Δ = 102-4·(-6)·12
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{97}}{2*-6}=\frac{-10-2\sqrt{97}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{97}}{2*-6}=\frac{-10+2\sqrt{97}}{-12}
$