3/4x+150=2x

Solution for 3/4x+150=2x equation:

3/4x+150=2x

We move all terms to the left:

3/4x+150-(2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+3/4x+150=0

We multiply all the terms by the denominator


-2x*4x+150*4x+3=0

Wy multiply elements

-8x^2+600x+3=0

a = -8; b = 600; c = +3;
Δ = b2-4ac
Δ = 6002-4·(-8)·3
Δ = 360096
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:

$\sqrt{\Delta}=\sqrt{360096}=\sqrt{1936*186}=\sqrt{1936}*\sqrt{186}=44\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-44\sqrt{186}}{2*-8}=\frac{-600-44\sqrt{186}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+44\sqrt{186}}{2*-8}=\frac{-600+44\sqrt{186}}{-16}
$