8x-6=6(x+3)6x

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

8x-6=6(x+3)6x

We move all terms to the left:

8x-6-(6(x+3)6x)=0


We calculate terms in parentheses: -(6(x+3)6x), so:

6(x+3)6x

We multiply parentheses

36x^2+108x

Back to the equation:

-(36x^2+108x)


We get rid of parentheses

-36x^2+8x-108x-6=0

We add all the numbers together, and all the variables

-36x^2-100x-6=0

a = -36; b = -100; c = -6;
Δ = b2-4ac
Δ = -1002-4·(-36)·(-6)
Δ = 9136
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:

$\sqrt{\Delta}=\sqrt{9136}=\sqrt{16*571}=\sqrt{16}*\sqrt{571}=4\sqrt{571}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{571}}{2*-36}=\frac{100-4\sqrt{571}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{571}}{2*-36}=\frac{100+4\sqrt{571}}{-72}
$