x-3/4x=4.5

Solution for x-3/4x=4.5 equation:

x-3/4x=4.5

We move all terms to the left:

x-3/4x-(4.5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x-3/4x-4.5=0

We multiply all the terms by the denominator


x*4x-(4.5)*4x-3=0

We multiply parentheses

x*4x-18x-3=0

Wy multiply elements

4x^2-18x-3=0

a = 4; b = -18; c = -3;
Δ = b2-4ac
Δ = -182-4·4·(-3)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*4}=\frac{18-2\sqrt{93}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*4}=\frac{18+2\sqrt{93}}{8}
$