x+(3/4)*x+(2/3)*x=200

Solution for x+(3/4)*x+(2/3)*x=200 equation:

x+(3/4)*x+(2/3)*x=200

We move all terms to the left:

x+(3/4)*x+(2/3)*x-(200)=0


Domain of the equation: 4)*x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+3/4)*x+(+2/3)*x-200=0

We multiply parentheses

3x^2+2x^2+x-200=0

We add all the numbers together, and all the variables

5x^2+x-200=0

a = 5; b = 1; c = -200;
Δ = b2-4ac
Δ = 12-4·5·(-200)
Δ = 4001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{4001}}{2*5}=\frac{-1-\sqrt{4001}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{4001}}{2*5}=\frac{-1+\sqrt{4001}}{10}
$