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x-14/3x+24=0

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Solution for x-14/3x+24=0 equation:



x-14/3x+24=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We multiply all the terms by the denominator
x*3x+24*3x-14=0
Wy multiply elements
3x^2+72x-14=0
a = 3; b = 72; c = -14;
Δ = b2-4ac
Δ = 722-4·3·(-14)
Δ = 5352
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{5352}=\sqrt{4*1338}=\sqrt{4}*\sqrt{1338}=2\sqrt{1338}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1338}}{2*3}=\frac{-72-2\sqrt{1338}}{6}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1338}}{2*3}=\frac{-72+2\sqrt{1338}}{6}

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