3x+2+x+2+1/2x+2=69

Solution for 3x+2+x+2+1/2x+2=69 equation:

3x+2+x+2+1/2x+2=69

We move all terms to the left:

3x+2+x+2+1/2x+2-(69)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/2x-63=0

We multiply all the terms by the denominator


4x*2x-63*2x+1=0

Wy multiply elements

8x^2-126x+1=0

a = 8; b = -126; c = +1;
Δ = b2-4ac
Δ = -1262-4·8·1
Δ = 15844
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:

$\sqrt{\Delta}=\sqrt{15844}=\sqrt{4*3961}=\sqrt{4}*\sqrt{3961}=2\sqrt{3961}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3961}}{2*8}=\frac{126-2\sqrt{3961}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3961}}{2*8}=\frac{126+2\sqrt{3961}}{16}
$