3x-1/2x=25

Solution for 3x-1/2x=25 equation:

3x-1/2x=25

We move all terms to the left:

3x-1/2x-(25)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-25*2x-1=0

Wy multiply elements

6x^2-50x-1=0

a = 6; b = -50; c = -1;
Δ = b2-4ac
Δ = -502-4·6·(-1)
Δ = 2524
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:

$\sqrt{\Delta}=\sqrt{2524}=\sqrt{4*631}=\sqrt{4}*\sqrt{631}=2\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{631}}{2*6}=\frac{50-2\sqrt{631}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{631}}{2*6}=\frac{50+2\sqrt{631}}{12}
$