2x+3(2x)+1/2x=76

Solution for 2x+3(2x)+1/2x=76 equation:

2x+3(2x)+1/2x=76

We move all terms to the left:

2x+3(2x)+1/2x-(76)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

34x+1/2x-76=0

We multiply all the terms by the denominator


34x*2x-76*2x+1=0

Wy multiply elements

68x^2-152x+1=0

a = 68; b = -152; c = +1;
Δ = b2-4ac
Δ = -1522-4·68·1
Δ = 22832
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:

$\sqrt{\Delta}=\sqrt{22832}=\sqrt{16*1427}=\sqrt{16}*\sqrt{1427}=4\sqrt{1427}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-152)-4\sqrt{1427}}{2*68}=\frac{152-4\sqrt{1427}}{136}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-152)+4\sqrt{1427}}{2*68}=\frac{152+4\sqrt{1427}}{136}
$