3/4c-1/4c+3=7c=

Solution for 3/4c-1/4c+3=7c= equation:

3/4c-1/4c+3=7c=

We move all terms to the left:

3/4c-1/4c+3-(7c)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R


We add all the numbers together, and all the variables

-7c+3/4c-1/4c+3=0

We multiply all the terms by the denominator


-7c*4c+3*4c+3-1=0

We add all the numbers together, and all the variables

-7c*4c+3*4c+2=0

Wy multiply elements

-28c^2+12c+2=0

a = -28; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-28)·2
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{23}}{2*-28}=\frac{-12-4\sqrt{23}}{-56}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{23}}{2*-28}=\frac{-12+4\sqrt{23}}{-56}
$