X+1=3/4x+6

Solution for X+1=3/4x+6 equation:

X+1=3/4X+6

We move all terms to the left:

X+1-(3/4X+6)=0


Domain of the equation: 4X+6)!=0

X∈R


We get rid of parentheses

X-3/4X-6+1=0

We multiply all the terms by the denominator


X*4X-6*4X+1*4X-3=0

Wy multiply elements

4X^2-24X+4X-3=0

We add all the numbers together, and all the variables

4X^2-20X-3=0

a = 4; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·4·(-3)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{7}}{2*4}=\frac{20-8\sqrt{7}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{7}}{2*4}=\frac{20+8\sqrt{7}}{8}
$