5x-7/3x=-4

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Solution for 5x-7/3x=-4 equation:



5x-7/3x=-4
We move all terms to the left:
5x-7/3x-(-4)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
5x-7/3x+4=0
We multiply all the terms by the denominator
5x*3x+4*3x-7=0
Wy multiply elements
15x^2+12x-7=0
a = 15; b = 12; c = -7;
Δ = b2-4ac
Δ = 122-4·15·(-7)
Δ = 564
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:
$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{141}}{2*15}=\frac{-12-2\sqrt{141}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{141}}{2*15}=\frac{-12+2\sqrt{141}}{30} $

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