2x+85=3/4x

Solution for 2x+85=3/4x equation:

2x+85=3/4x

We move all terms to the left:

2x+85-(3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+3/4x)+85=0

We get rid of parentheses

2x-3/4x+85=0

We multiply all the terms by the denominator


2x*4x+85*4x-3=0

Wy multiply elements

8x^2+340x-3=0

a = 8; b = 340; c = -3;
Δ = b2-4ac
Δ = 3402-4·8·(-3)
Δ = 115696
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:

$\sqrt{\Delta}=\sqrt{115696}=\sqrt{16*7231}=\sqrt{16}*\sqrt{7231}=4\sqrt{7231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(340)-4\sqrt{7231}}{2*8}=\frac{-340-4\sqrt{7231}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(340)+4\sqrt{7231}}{2*8}=\frac{-340+4\sqrt{7231}}{16}
$