5/9*x-32=100

Solution for 5/9*x-32=100 equation:

5/9*x-32=100

We move all terms to the left:

5/9*x-32-(100)=0


Domain of the equation: 9*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/9*x-132=0

We multiply all the terms by the denominator


-132*9*x+5=0

Wy multiply elements

-1188x*x+5=0

Wy multiply elements

-1188x^2+5=0

a = -1188; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-1188)·5
Δ = 23760
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:

$\sqrt{\Delta}=\sqrt{23760}=\sqrt{144*165}=\sqrt{144}*\sqrt{165}=12\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{165}}{2*-1188}=\frac{0-12\sqrt{165}}{-2376}
=-\frac{12\sqrt{165}}{-2376}
=-\frac{\sqrt{165}}{-198}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{165}}{2*-1188}=\frac{0+12\sqrt{165}}{-2376}
=\frac{12\sqrt{165}}{-2376}
=\frac{\sqrt{165}}{-198}
$