3x+1/2(3x)+x=480

Solution for 3x+1/2(3x)+x=480 equation:

3x+1/2(3x)+x=480

We move all terms to the left:

3x+1/2(3x)+x-(480)=0


Domain of the equation: 23x!=0

x!=0/23

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/23x-480=0

We multiply all the terms by the denominator


4x*23x-480*23x+1=0

Wy multiply elements

92x^2-11040x+1=0

a = 92; b = -11040; c = +1;
Δ = b2-4ac
Δ = -110402-4·92·1
Δ = 121881232
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:

$\sqrt{\Delta}=\sqrt{121881232}=\sqrt{16*7617577}=\sqrt{16}*\sqrt{7617577}=4\sqrt{7617577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11040)-4\sqrt{7617577}}{2*92}=\frac{11040-4\sqrt{7617577}}{184}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11040)+4\sqrt{7617577}}{2*92}=\frac{11040+4\sqrt{7617577}}{184}
$