3x+3/2x=10

Solution for 3x+3/2x=10 equation:

3x+3/2x=10

We move all terms to the left:

3x+3/2x-(10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-10*2x+3=0

Wy multiply elements

6x^2-20x+3=0

a = 6; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·6·3
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{82}}{2*6}=\frac{20-2\sqrt{82}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{82}}{2*6}=\frac{20+2\sqrt{82}}{12}
$