(1/4)x=2x+17.5

Solution for (1/4)x=2x+17.5 equation:

(1/4)x=2x+17.5

We move all terms to the left:

(1/4)x-(2x+17.5)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)x-(2x+17.5)=0

We multiply parentheses

x^2-(2x+17.5)=0

We get rid of parentheses

x^2-2x-17.5=0

a = 1; b = -2; c = -17.5;
Δ = b2-4ac
Δ = -22-4·1·(-17.5)
Δ = 74
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{-(-2)-\sqrt{74}}{2*1}=\frac{2-\sqrt{74}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{74}}{2*1}=\frac{2+\sqrt{74}}{2}
$