150=x+3/4x

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

150=x+3/4x

We move all terms to the left:

150-(x+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 = 359952
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:

$\sqrt{\Delta}=\sqrt{359952}=\sqrt{16*22497}=\sqrt{16}*\sqrt{22497}=4\sqrt{22497}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-4\sqrt{22497}}{2*-4}=\frac{-600-4\sqrt{22497}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+4\sqrt{22497}}{2*-4}=\frac{-600+4\sqrt{22497}}{-8}
$