0.5x+(1)/(4)x=13.5

Solution for 0.5x+(1)/(4)x=13.5 equation:

0.5x+(1)/(4)x=13.5

We move all terms to the left:

0.5x+(1)/(4)x-(13.5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

0.5x+1/4x-13.5=0

We multiply all the terms by the denominator


(0.5x)*4x-(13.5)*4x+1=0

We add all the numbers together, and all the variables

(+0.5x)*4x-(13.5)*4x+1=0

We multiply parentheses

0x^2-54x+1=0

We add all the numbers together, and all the variables

x^2-54x+1=0

a = 1; b = -54; c = +1;
Δ = b2-4ac
Δ = -542-4·1·1
Δ = 2912
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:

$\sqrt{\Delta}=\sqrt{2912}=\sqrt{16*182}=\sqrt{16}*\sqrt{182}=4\sqrt{182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-4\sqrt{182}}{2*1}=\frac{54-4\sqrt{182}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+4\sqrt{182}}{2*1}=\frac{54+4\sqrt{182}}{2}
$