(2/3)x+1/4=x+3

Solution for (2/3)x+1/4=x+3 equation:

(2/3)x+1/4=x+3

We move all terms to the left:

(2/3)x+1/4-(x+3)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)x-(x+3)+1/4=0

We multiply parentheses

2x^2-(x+3)+1/4=0

We get rid of parentheses

2x^2-x-3+1/4=0

We multiply all the terms by the denominator


2x^2*4-x*4+1-3*4=0

We add all the numbers together, and all the variables

2x^2*4-x*4-11=0

Wy multiply elements

8x^2-4x-11=0

a = 8; b = -4; c = -11;
Δ = b2-4ac
Δ = -42-4·8·(-11)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{23}}{2*8}=\frac{4-4\sqrt{23}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{23}}{2*8}=\frac{4+4\sqrt{23}}{16}
$