X+3/3x-15=10

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Solution for X+3/3x-15=10 equation:



X+3/3X-15=10
We move all terms to the left:
X+3/3X-15-(10)=0
Domain of the equation: 3X!=0
X!=0/3
X!=0
X∈R
We add all the numbers together, and all the variables
X+3/3X-25=0
We multiply all the terms by the denominator
X*3X-25*3X+3=0
Wy multiply elements
3X^2-75X+3=0
a = 3; b = -75; c = +3;
Δ = b2-4ac
Δ = -752-4·3·3
Δ = 5589
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:
$\sqrt{\Delta}=\sqrt{5589}=\sqrt{81*69}=\sqrt{81}*\sqrt{69}=9\sqrt{69}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-9\sqrt{69}}{2*3}=\frac{75-9\sqrt{69}}{6} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+9\sqrt{69}}{2*3}=\frac{75+9\sqrt{69}}{6} $

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