2(x)+2/3(x)=96

Solution for 2(x)+2/3(x)=96 equation:

2(x)+2/3(x)=96

We move all terms to the left:

2(x)+2/3(x)-(96)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-96*3x+2=0

Wy multiply elements

6x^2-288x+2=0

a = 6; b = -288; c = +2;
Δ = b2-4ac
Δ = -2882-4·6·2
Δ = 82896
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:

$\sqrt{\Delta}=\sqrt{82896}=\sqrt{16*5181}=\sqrt{16}*\sqrt{5181}=4\sqrt{5181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-4\sqrt{5181}}{2*6}=\frac{288-4\sqrt{5181}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+4\sqrt{5181}}{2*6}=\frac{288+4\sqrt{5181}}{12}
$