x+2*x+(1/2)x+(1/4)x+3=300

Solution for x+2*x+(1/2)x+(1/4)x+3=300 equation:

x+2x+(1/2)x+(1/4)x+3=300

We move all terms to the left:

x+2x+(1/2)x+(1/4)x+3-(300)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+2x+(+1/2)x+(+1/4)x+3-300=0

We add all the numbers together, and all the variables

3x+(+1/2)x+(+1/4)x-297=0

We multiply parentheses

x^2+x^2+3x-297=0

We add all the numbers together, and all the variables

2x^2+3x-297=0

a = 2; b = 3; c = -297;
Δ = b2-4ac
Δ = 32-4·2·(-297)
Δ = 2385
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:

$\sqrt{\Delta}=\sqrt{2385}=\sqrt{9*265}=\sqrt{9}*\sqrt{265}=3\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{265}}{2*2}=\frac{-3-3\sqrt{265}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{265}}{2*2}=\frac{-3+3\sqrt{265}}{4}
$