7x-32/x-32=5

Solution for 7x-32/x-32=5 equation:

7x-32/x-32=5

We move all terms to the left:

7x-32/x-32-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7x-32/x-37=0

We multiply all the terms by the denominator


7x*x-37*x-32=0

We add all the numbers together, and all the variables

-37x+7x*x-32=0

Wy multiply elements

7x^2-37x-32=0

a = 7; b = -37; c = -32;
Δ = b2-4ac
Δ = -372-4·7·(-32)
Δ = 2265
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{-(-37)-\sqrt{2265}}{2*7}=\frac{37-\sqrt{2265}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{2265}}{2*7}=\frac{37+\sqrt{2265}}{14}
$