(5x)(18,5/3x)=29,70

Solution for (5x)(18,5/3x)=29,70 equation:

(5x)(18.5/3x)=29.70

We move all terms to the left:

(5x)(18.5/3x)-(29.70)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x(+18.5/3x)-(29.7)=0

We add all the numbers together, and all the variables

5x(+18.5/3x)-29.7=0

We multiply parentheses

90x^2-29.7=0

a = 90; b = 0; c = -29.7;
Δ = b2-4ac
Δ = 02-4·90·(-29.7)
Δ = 10692
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:

$\sqrt{\Delta}=\sqrt{10692}=\sqrt{324*33}=\sqrt{324}*\sqrt{33}=18\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{33}}{2*90}=\frac{0-18\sqrt{33}}{180}
=-\frac{18\sqrt{33}}{180}
=-\frac{\sqrt{33}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{33}}{2*90}=\frac{0+18\sqrt{33}}{180}
=\frac{18\sqrt{33}}{180}
=\frac{\sqrt{33}}{10}
$