X+150=3/4x

Solution for X+150=3/4x equation:

X+150=3/4X

We move all terms to the left:

X+150-(3/4X)=0


Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+3/4X)+150=0

We get rid of parentheses

X-3/4X+150=0

We multiply all the terms by the denominator


X*4X+150*4X-3=0

Wy multiply elements

4X^2+600X-3=0

a = 4; b = 600; c = -3;
Δ = b2-4ac
Δ = 6002-4·4·(-3)
Δ = 360048
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:

$\sqrt{\Delta}=\sqrt{360048}=\sqrt{16*22503}=\sqrt{16}*\sqrt{22503}=4\sqrt{22503}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-4\sqrt{22503}}{2*4}=\frac{-600-4\sqrt{22503}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+4\sqrt{22503}}{2*4}=\frac{-600+4\sqrt{22503}}{8}
$