3/2x+x=25

Solution for 3/2x+x=25 equation:

3/2x+x=25

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/2x-25=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-50x+3=0

a = 2; b = -50; c = +3;
Δ = b2-4ac
Δ = -502-4·2·3
Δ = 2476
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:

$\sqrt{\Delta}=\sqrt{2476}=\sqrt{4*619}=\sqrt{4}*\sqrt{619}=2\sqrt{619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{619}}{2*2}=\frac{50-2\sqrt{619}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{619}}{2*2}=\frac{50+2\sqrt{619}}{4}
$