3/2x+x=50

Solution for 3/2x+x=50 equation:

3/2x+x=50

We move all terms to the left:

3/2x+x-(50)=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-50=0

We multiply all the terms by the denominator


x*2x-50*2x+3=0

Wy multiply elements

2x^2-100x+3=0

a = 2; b = -100; c = +3;
Δ = b2-4ac
Δ = -1002-4·2·3
Δ = 9976
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:

$\sqrt{\Delta}=\sqrt{9976}=\sqrt{4*2494}=\sqrt{4}*\sqrt{2494}=2\sqrt{2494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2494}}{2*2}=\frac{100-2\sqrt{2494}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2494}}{2*2}=\frac{100+2\sqrt{2494}}{4}
$