6/7*c=8

Solution for 6/7*c=8 equation:

6/7*c=8

We move all terms to the left:

6/7*c-(8)=0


Domain of the equation: 7*c!=0

c!=0/1

c!=0

c∈R


We multiply all the terms by the denominator


-8*7*c+6=0

Wy multiply elements

-56c*c+6=0

Wy multiply elements

-56c^2+6=0

a = -56; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-56)·6
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{21}}{2*-56}=\frac{0-8\sqrt{21}}{-112}
=-\frac{8\sqrt{21}}{-112}
=-\frac{\sqrt{21}}{-14}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{21}}{2*-56}=\frac{0+8\sqrt{21}}{-112}
=\frac{8\sqrt{21}}{-112}
=\frac{\sqrt{21}}{-14}
$