3x+900=5/2x+1200

Solution for 3x+900=5/2x+1200 equation:

3x+900=5/2x+1200

We move all terms to the left:

3x+900-(5/2x+1200)=0


Domain of the equation: 2x+1200)!=0

x∈R


We get rid of parentheses

3x-5/2x-1200+900=0

We multiply all the terms by the denominator


3x*2x-1200*2x+900*2x-5=0

Wy multiply elements

6x^2-2400x+1800x-5=0

We add all the numbers together, and all the variables

6x^2-600x-5=0

a = 6; b = -600; c = -5;
Δ = b2-4ac
Δ = -6002-4·6·(-5)
Δ = 360120
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:

$\sqrt{\Delta}=\sqrt{360120}=\sqrt{4*90030}=\sqrt{4}*\sqrt{90030}=2\sqrt{90030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-2\sqrt{90030}}{2*6}=\frac{600-2\sqrt{90030}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+2\sqrt{90030}}{2*6}=\frac{600+2\sqrt{90030}}{12}
$