3/2x*5x=13

Solution for 3/2x*5x=13 equation:

3/2x*5x=13

We move all terms to the left:

3/2x*5x-(13)=0


Domain of the equation: 2x*5x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-13*2x*5x+3=0

Wy multiply elements

-130x^2*5+3=0

Wy multiply elements

-650x^2+3=0

a = -650; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-650)·3
Δ = 7800
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:

$\sqrt{\Delta}=\sqrt{7800}=\sqrt{100*78}=\sqrt{100}*\sqrt{78}=10\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{78}}{2*-650}=\frac{0-10\sqrt{78}}{-1300}
=-\frac{10\sqrt{78}}{-1300}
=-\frac{\sqrt{78}}{-130}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{78}}{2*-650}=\frac{0+10\sqrt{78}}{-1300}
=\frac{10\sqrt{78}}{-1300}
=\frac{\sqrt{78}}{-130}
$