/x+37=x+67

Solution for /x+37=x+67 equation:

/x+37=x+67

We move all terms to the left:

/x+37-(x+67)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

/x-x-67+37=0

We multiply all the terms by the denominator


-x*x-67*x+37*x+=0

We add all the numbers together, and all the variables

-30x-x*x=0

Wy multiply elements

-1x^2-30x=0

a = -1; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·(-1)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*-1}=\frac{60}{-2}
=-30
$