x-5=3/4x+1

Solution for x-5=3/4x+1 equation:

x-5=3/4x+1

We move all terms to the left:

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


Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-24x-3=0

a = 4; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·4·(-3)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*4}=\frac{24-4\sqrt{39}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*4}=\frac{24+4\sqrt{39}}{8}
$