144/x=x+7

Solution for 144/x=x+7 equation:

144/x=x+7

We move all terms to the left:

144/x-(x+7)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

144/x-x-7=0

We multiply all the terms by the denominator


-x*x-7*x+144=0

We add all the numbers together, and all the variables

-7x-x*x+144=0

Wy multiply elements

-1x^2-7x+144=0

a = -1; b = -7; c = +144;
Δ = b2-4ac
Δ = -72-4·(-1)·144
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-25}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+25}{2*-1}=\frac{32}{-2}
=-16
$