(1/4)x+(5/10)x=200

Solution for (1/4)x+(5/10)x=200 equation:

(1/4)x+(5/10)x=200

We move all terms to the left:

(1/4)x+(5/10)x-(200)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 10)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)x+(+5/10)x-200=0

We multiply parentheses

x^2+5x^2-200=0

We add all the numbers together, and all the variables

6x^2-200=0

a = 6; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·6·(-200)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3}}{2*6}=\frac{0-40\sqrt{3}}{12}
=-\frac{40\sqrt{3}}{12}
=-\frac{10\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3}}{2*6}=\frac{0+40\sqrt{3}}{12}
=\frac{40\sqrt{3}}{12}
=\frac{10\sqrt{3}}{3}
$