4+10/x=x+7

Solution for 4+10/x=x+7 equation:

4+10/x=x+7

We move all terms to the left:

4+10/x-(x+7)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

10/x-x-7+4=0

We multiply all the terms by the denominator


-x*x-7*x+4*x+10=0

We add all the numbers together, and all the variables

-3x-x*x+10=0

Wy multiply elements

-1x^2-3x+10=0

a = -1; b = -3; c = +10;
Δ = b2-4ac
Δ = -32-4·(-1)·10
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*-1}=\frac{10}{-2}
=-5
$