3x=5*35/69X

Solution for 3x=5*35/69X equation:

3x=5*35/69x

We move all terms to the left:

3x-(5*35/69x)=0


Domain of the equation: 69x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+5*35/69x)=0

We get rid of parentheses

3x-5*35/69x=0

We multiply all the terms by the denominator


3x*69x-5*35=0

We add all the numbers together, and all the variables

3x*69x-175=0

Wy multiply elements

207x^2-175=0

a = 207; b = 0; c = -175;
Δ = b2-4ac
Δ = 02-4·207·(-175)
Δ = 144900
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:

$\sqrt{\Delta}=\sqrt{144900}=\sqrt{900*161}=\sqrt{900}*\sqrt{161}=30\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{161}}{2*207}=\frac{0-30\sqrt{161}}{414}
=-\frac{30\sqrt{161}}{414}
=-\frac{5\sqrt{161}}{69}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{161}}{2*207}=\frac{0+30\sqrt{161}}{414}
=\frac{30\sqrt{161}}{414}
=\frac{5\sqrt{161}}{69}
$