(-1/2c)7=1/4c-7

Solution for (-1/2c)7=1/4c-7 equation:

(-1/2c)7=1/4c-7

We move all terms to the left:

(-1/2c)7-(1/4c-7)=0


Domain of the equation: 2c)7!=0

c!=0/1

c!=0

c∈R



Domain of the equation: 4c-7)!=0

c∈R


We multiply parentheses

-7c-(1/4c-7)=0

We get rid of parentheses

-7c-1/4c+7=0

We multiply all the terms by the denominator


-7c*4c+7*4c-1=0

Wy multiply elements

-28c^2+28c-1=0

a = -28; b = 28; c = -1;
Δ = b2-4ac
Δ = 282-4·(-28)·(-1)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{42}}{2*-28}=\frac{-28-4\sqrt{42}}{-56}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{42}}{2*-28}=\frac{-28+4\sqrt{42}}{-56}
$