8-7/10c=6+1/5c

Solution for 8-7/10c=6+1/5c equation:

8-7/10c=6+1/5c

We move all terms to the left:

8-7/10c-(6+1/5c)=0


Domain of the equation: 10c!=0

c!=0/10

c!=0

c∈R



Domain of the equation: 5c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

-7/10c-(1/5c+6)+8=0

We get rid of parentheses

-7/10c-1/5c-6+8=0

We calculate fractions


(-35c)/50c^2+(-10c)/50c^2-6+8=0

We add all the numbers together, and all the variables

(-35c)/50c^2+(-10c)/50c^2+2=0

We multiply all the terms by the denominator


(-35c)+(-10c)+2*50c^2=0

Wy multiply elements

100c^2+(-35c)+(-10c)=0

We get rid of parentheses

100c^2-35c-10c=0

We add all the numbers together, and all the variables

100c^2-45c=0

a = 100; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·100·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*100}=\frac{0}{200}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*100}=\frac{90}{200}
=9/20
$