84/2x=3x-29

Solution for 84/2x=3x-29 equation:

84/2x=3x-29

We move all terms to the left:

84/2x-(3x-29)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

84/2x-3x+29=0

We multiply all the terms by the denominator


-3x*2x+29*2x+84=0

Wy multiply elements

-6x^2+58x+84=0

a = -6; b = 58; c = +84;
Δ = b2-4ac
Δ = 582-4·(-6)·84
Δ = 5380
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:

$\sqrt{\Delta}=\sqrt{5380}=\sqrt{4*1345}=\sqrt{4}*\sqrt{1345}=2\sqrt{1345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{1345}}{2*-6}=\frac{-58-2\sqrt{1345}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{1345}}{2*-6}=\frac{-58+2\sqrt{1345}}{-12}
$