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3x+2/4x=24
We move all terms to the left:
3x+2/4x-(24)=0
Domain of the equation: 4x!=0We multiply all the terms by the denominator
x!=0/4
x!=0
x∈R
3x*4x-24*4x+2=0
Wy multiply elements
12x^2-96x+2=0
a = 12; b = -96; c = +2;
Δ = b2-4ac
Δ = -962-4·12·2
Δ = 9120
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9120}=\sqrt{16*570}=\sqrt{16}*\sqrt{570}=4\sqrt{570}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{570}}{2*12}=\frac{96-4\sqrt{570}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{570}}{2*12}=\frac{96+4\sqrt{570}}{24} $
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