2/3*c=25

Solution for 2/3*c=25 equation:

2/3*c=25

We move all terms to the left:

2/3*c-(25)=0


Domain of the equation: 3*c!=0

c!=0/1

c!=0

c∈R


We multiply all the terms by the denominator


-25*3*c+2=0

Wy multiply elements

-75c*c+2=0

Wy multiply elements

-75c^2+2=0

a = -75; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-75)·2
Δ = 600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-75}=\frac{0-10\sqrt{6}}{-150}
=-\frac{10\sqrt{6}}{-150}
=-\frac{\sqrt{6}}{-15}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-75}=\frac{0+10\sqrt{6}}{-150}
=\frac{10\sqrt{6}}{-150}
=\frac{\sqrt{6}}{-15}
$