4x+3/4x=2x+17

Solution for 4x+3/4x=2x+17 equation:

4x+3/4x=2x+17

We move all terms to the left:

4x+3/4x-(2x+17)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

4x+3/4x-2x-17=0

We multiply all the terms by the denominator


4x*4x-2x*4x-17*4x+3=0

Wy multiply elements

16x^2-8x^2-68x+3=0

We add all the numbers together, and all the variables

8x^2-68x+3=0

a = 8; b = -68; c = +3;
Δ = b2-4ac
Δ = -682-4·8·3
Δ = 4528
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:

$\sqrt{\Delta}=\sqrt{4528}=\sqrt{16*283}=\sqrt{16}*\sqrt{283}=4\sqrt{283}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{283}}{2*8}=\frac{68-4\sqrt{283}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{283}}{2*8}=\frac{68+4\sqrt{283}}{16}
$