x-4/4=3/4x-5

Solution for x-4/4=3/4x-5 equation:

x-4/4=3/4x-5

We move all terms to the left:

x-4/4-(3/4x-5)=0


Domain of the equation: 4x-5)!=0

x∈R


We add all the numbers together, and all the variables

x-(3/4x-5)-1=0

We get rid of parentheses

x-3/4x+5-1=0

We multiply all the terms by the denominator


x*4x+5*4x-1*4x-3=0

Wy multiply elements

4x^2+20x-4x-3=0

We add all the numbers together, and all the variables

4x^2+16x-3=0

a = 4; b = 16; c = -3;
Δ = b2-4ac
Δ = 162-4·4·(-3)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{19}}{2*4}=\frac{-16-4\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{19}}{2*4}=\frac{-16+4\sqrt{19}}{8}
$