(5/3)x=35/3

Solution for (5/3)x=35/3 equation:

(5/3)x=35/3

We move all terms to the left:

(5/3)x-(35/3)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/3)x-(+35/3)=0

We multiply parentheses

5x^2-(+35/3)=0

We get rid of parentheses

5x^2-35/3=0

We multiply all the terms by the denominator


5x^2*3-35=0

Wy multiply elements

15x^2-35=0

a = 15; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·15·(-35)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{21}}{2*15}=\frac{0-10\sqrt{21}}{30}
=-\frac{10\sqrt{21}}{30}
=-\frac{\sqrt{21}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{21}}{2*15}=\frac{0+10\sqrt{21}}{30}
=\frac{10\sqrt{21}}{30}
=\frac{\sqrt{21}}{3}
$