3/4x+5=x+6

Solution for 3/4x+5=x+6 equation:

3/4x+5=x+6

We move all terms to the left:

3/4x+5-(x+6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-x-6+5=0

We multiply all the terms by the denominator


-x*4x-6*4x+5*4x+3=0

Wy multiply elements

-4x^2-24x+20x+3=0

We add all the numbers together, and all the variables

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

a = -4; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-4)·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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