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3/4x+5-12x=3
We move all terms to the left:
3/4x+5-12x-(3)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
-12x+3/4x+2=0
We multiply all the terms by the denominator
-12x*4x+2*4x+3=0
Wy multiply elements
-48x^2+8x+3=0
a = -48; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·(-48)·3
Δ = 640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{10}}{2*-48}=\frac{-8-8\sqrt{10}}{-96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{10}}{2*-48}=\frac{-8+8\sqrt{10}}{-96} $
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