4x+3/2x=85

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

4x+3/2x=85

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-170x+3=0

a = 8; b = -170; c = +3;
Δ = b2-4ac
Δ = -1702-4·8·3
Δ = 28804
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:

$\sqrt{\Delta}=\sqrt{28804}=\sqrt{4*7201}=\sqrt{4}*\sqrt{7201}=2\sqrt{7201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-2\sqrt{7201}}{2*8}=\frac{170-2\sqrt{7201}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+2\sqrt{7201}}{2*8}=\frac{170+2\sqrt{7201}}{16}
$