345+5x=180/x*27

Solution for 345+5x=180/x*27 equation:

345+5x=180/x*27

We move all terms to the left:

345+5x-(180/x*27)=0


Domain of the equation: x*27)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+180/x*27)+345=0

We get rid of parentheses

5x-180/x*27+345=0

We multiply all the terms by the denominator


5x*x*27+345*x*27-180=0

Wy multiply elements

135x^2*2+9315x*2-180=0

Wy multiply elements

270x^2+18630x-180=0

a = 270; b = 18630; c = -180;
Δ = b2-4ac
Δ = 186302-4·270·(-180)
Δ = 347271300
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:

$\sqrt{\Delta}=\sqrt{347271300}=\sqrt{8100*42873}=\sqrt{8100}*\sqrt{42873}=90\sqrt{42873}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18630)-90\sqrt{42873}}{2*270}=\frac{-18630-90\sqrt{42873}}{540}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18630)+90\sqrt{42873}}{2*270}=\frac{-18630+90\sqrt{42873}}{540}
$