7.1/6x=2x+5

Solution for 7.1/6x=2x+5 equation:

7.1/6x=2x+5

We move all terms to the left:

7.1/6x-(2x+5)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

7.1/6x-2x-5=0

We multiply all the terms by the denominator


-2x*6x-5*6x+7.1=0

Wy multiply elements

-12x^2-30x+7.1=0

a = -12; b = -30; c = +7.1;
Δ = b2-4ac
Δ = -302-4·(-12)·7.1
Δ = 1240.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-\sqrt{1240.8}}{2*-12}=\frac{30-\sqrt{1240.8}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{1240.8}}{2*-12}=\frac{30+\sqrt{1240.8}}{-24}
$