m+1/5m=90

Solution for m+1/5m=90 equation:

m+1/5m=90

We move all terms to the left:

m+1/5m-(90)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We multiply all the terms by the denominator


m*5m-90*5m+1=0

Wy multiply elements

5m^2-450m+1=0

a = 5; b = -450; c = +1;
Δ = b2-4ac
Δ = -4502-4·5·1
Δ = 202480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{202480}=\sqrt{16*12655}=\sqrt{16}*\sqrt{12655}=4\sqrt{12655}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-4\sqrt{12655}}{2*5}=\frac{450-4\sqrt{12655}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+4\sqrt{12655}}{2*5}=\frac{450+4\sqrt{12655}}{10}
$