14c-7/8c=5

Solution for 14c-7/8c=5 equation:

14c-7/8c=5

We move all terms to the left:

14c-7/8c-(5)=0


Domain of the equation: 8c!=0

c!=0/8

c!=0

c∈R


We multiply all the terms by the denominator


14c*8c-5*8c-7=0

Wy multiply elements

112c^2-40c-7=0

a = 112; b = -40; c = -7;
Δ = b2-4ac
Δ = -402-4·112·(-7)
Δ = 4736
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:

$\sqrt{\Delta}=\sqrt{4736}=\sqrt{64*74}=\sqrt{64}*\sqrt{74}=8\sqrt{74}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{74}}{2*112}=\frac{40-8\sqrt{74}}{224}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{74}}{2*112}=\frac{40+8\sqrt{74}}{224}
$