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x-3/4x=4.5
We move all terms to the left:
x-3/4x-(4.5)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
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} $
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