3/x+1=2x-7

Solution for 3/x+1=2x-7 equation:

3/x+1=2x-7

We move all terms to the left:

3/x+1-(2x-7)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

3/x-2x+7+1=0

We multiply all the terms by the denominator


-2x*x+7*x+1*x+3=0

We add all the numbers together, and all the variables

8x-2x*x+3=0

Wy multiply elements

-2x^2+8x+3=0

a = -2; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·(-2)·3
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{22}}{2*-2}=\frac{-8-2\sqrt{22}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{22}}{2*-2}=\frac{-8+2\sqrt{22}}{-4}
$