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1/4x=3x-44
We move all terms to the left:
1/4x-(3x-44)=0
Domain of the equation: 4x!=0We get rid of parentheses
x!=0/4
x!=0
x∈R
1/4x-3x+44=0
We multiply all the terms by the denominator
-3x*4x+44*4x+1=0
Wy multiply elements
-12x^2+176x+1=0
a = -12; b = 176; c = +1;
Δ = b2-4ac
Δ = 1762-4·(-12)·1
Δ = 31024
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31024}=\sqrt{16*1939}=\sqrt{16}*\sqrt{1939}=4\sqrt{1939}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-4\sqrt{1939}}{2*-12}=\frac{-176-4\sqrt{1939}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+4\sqrt{1939}}{2*-12}=\frac{-176+4\sqrt{1939}}{-24} $
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