4x-26=3/4x

Solution for 4x-26=3/4x equation:

4x-26=3/4x

We move all terms to the left:

4x-26-(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

4x-(+3/4x)-26=0

We get rid of parentheses

4x-3/4x-26=0

We multiply all the terms by the denominator


4x*4x-26*4x-3=0

Wy multiply elements

16x^2-104x-3=0

a = 16; b = -104; c = -3;
Δ = b2-4ac
Δ = -1042-4·16·(-3)
Δ = 11008
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:

$\sqrt{\Delta}=\sqrt{11008}=\sqrt{256*43}=\sqrt{256}*\sqrt{43}=16\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-16\sqrt{43}}{2*16}=\frac{104-16\sqrt{43}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+16\sqrt{43}}{2*16}=\frac{104+16\sqrt{43}}{32}
$