10/3*x=25

Solution for 10/3*x=25 equation:

10/3*x=25

We move all terms to the left:

10/3*x-(25)=0


Domain of the equation: 3*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-25*3*x+10=0

Wy multiply elements

-75x*x+10=0

Wy multiply elements

-75x^2+10=0

a = -75; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-75)·10
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{30}}{2*-75}=\frac{0-10\sqrt{30}}{-150}
=-\frac{10\sqrt{30}}{-150}
=-\frac{\sqrt{30}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{30}}{2*-75}=\frac{0+10\sqrt{30}}{-150}
=\frac{10\sqrt{30}}{-150}
=\frac{\sqrt{30}}{-15}
$