45=5/3*u

Solution for 45=5/3*u equation:

45=5/3*u

We move all terms to the left:

45-(5/3*u)=0


Domain of the equation: 3*u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

-(+5/3*u)+45=0

We get rid of parentheses

-5/3*u+45=0

We multiply all the terms by the denominator


45*3*u-5=0

Wy multiply elements

135u*u-5=0

Wy multiply elements

135u^2-5=0

a = 135; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·135·(-5)
Δ = 2700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{3}}{2*135}=\frac{0-30\sqrt{3}}{270}
=-\frac{30\sqrt{3}}{270}
=-\frac{\sqrt{3}}{9}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{3}}{2*135}=\frac{0+30\sqrt{3}}{270}
=\frac{30\sqrt{3}}{270}
=\frac{\sqrt{3}}{9}
$