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x+50=3/2x

We move all terms to the left:

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

Domain of the equation: 2x)!=0We add all the numbers together, and all the variables

x!=0/1

x!=0

x∈R

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

We get rid of parentheses

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 = b^{2}-4ac

Δ = 100^{2}-4·2·(-3)

Δ = 10024

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{10024}=\sqrt{4*2506}=\sqrt{4}*\sqrt{2506}=2\sqrt{2506}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2506}}{2*2}=\frac{-100-2\sqrt{2506}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2506}}{2*2}=\frac{-100+2\sqrt{2506}}{4} $

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