1/4x+.5x=1.5

Solution for 1/4x+.5x=1.5 equation:

1/4x+.5x=1.5

We move all terms to the left:

1/4x+.5x-(1.5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

.5x+1/4x-1.5=0

We multiply all the terms by the denominator


(.5x)*4x-(1.5)*4x+1=0

We add all the numbers together, and all the variables

(+.5x)*4x-(1.5)*4x+1=0

We multiply parentheses

4x^2-6x+1=0

a = 4; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·4·1
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{5}}{2*4}=\frac{6-2\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{5}}{2*4}=\frac{6+2\sqrt{5}}{8}
$