50=3/2c-c

Solution for 50=3/2c-c equation:

50=3/2c-c

We move all terms to the left:

50-(3/2c-c)=0


Domain of the equation: 2c-c)!=0

c∈R


We add all the numbers together, and all the variables

-(-1c+3/2c)+50=0

We get rid of parentheses

1c-3/2c+50=0

We multiply all the terms by the denominator


1c*2c+50*2c-3=0

Wy multiply elements

2c^2+100c-3=0

a = 2; b = 100; c = -3;
Δ = b2-4ac
Δ = 1002-4·2·(-3)
Δ = 10024
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:

$\sqrt{\Delta}=\sqrt{10024}=\sqrt{4*2506}=\sqrt{4}*\sqrt{2506}=2\sqrt{2506}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2506}}{2*2}=\frac{-100-2\sqrt{2506}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2506}}{2*2}=\frac{-100+2\sqrt{2506}}{4}
$