3/11x=6x-42

Solution for 3/11x=6x-42 equation:

3/11x=6x-42

We move all terms to the left:

3/11x-(6x-42)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We get rid of parentheses

3/11x-6x+42=0

We multiply all the terms by the denominator


-6x*11x+42*11x+3=0

Wy multiply elements

-66x^2+462x+3=0

a = -66; b = 462; c = +3;
Δ = b2-4ac
Δ = 4622-4·(-66)·3
Δ = 214236
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:

$\sqrt{\Delta}=\sqrt{214236}=\sqrt{36*5951}=\sqrt{36}*\sqrt{5951}=6\sqrt{5951}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(462)-6\sqrt{5951}}{2*-66}=\frac{-462-6\sqrt{5951}}{-132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(462)+6\sqrt{5951}}{2*-66}=\frac{-462+6\sqrt{5951}}{-132}
$