X+3/3x-15=10

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}
$