3x-4/(x+1)=10

Solution for 3x-4/(x+1)=10 equation:

3x-4/(x+1)=10

We move all terms to the left:

3x-4/(x+1)-(10)=0


Domain of the equation: (x+1)!=0

We move all terms containing x to the left, all other terms to the right

x!=-1

x∈R


We multiply all the terms by the denominator


3x*(x+1)-10*(x+1)-4=0

We multiply parentheses

3x^2+3x-10x-10-4=0

We add all the numbers together, and all the variables

3x^2-7x-14=0

a = 3; b = -7; c = -14;
Δ = b2-4ac
Δ = -72-4·3·(-14)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{217}}{2*3}=\frac{7-\sqrt{217}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{217}}{2*3}=\frac{7+\sqrt{217}}{6}
$