x+1=3/4x+4

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

x+1=3/4x+4

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-16x+4x-3=0

We add all the numbers together, and all the variables

4x^2-12x-3=0

a = 4; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·4·(-3)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*4}=\frac{12-8\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*4}=\frac{12+8\sqrt{3}}{8}
$