2x=3/17x-110

Solution for 2x=3/17x-110 equation:

2x=3/17x-110

We move all terms to the left:

2x-(3/17x-110)=0


Domain of the equation: 17x-110)!=0

x∈R


We get rid of parentheses

2x-3/17x+110=0

We multiply all the terms by the denominator


2x*17x+110*17x-3=0

Wy multiply elements

34x^2+1870x-3=0

a = 34; b = 1870; c = -3;
Δ = b2-4ac
Δ = 18702-4·34·(-3)
Δ = 3497308
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:

$\sqrt{\Delta}=\sqrt{3497308}=\sqrt{4*874327}=\sqrt{4}*\sqrt{874327}=2\sqrt{874327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1870)-2\sqrt{874327}}{2*34}=\frac{-1870-2\sqrt{874327}}{68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1870)+2\sqrt{874327}}{2*34}=\frac{-1870+2\sqrt{874327}}{68}
$