3c+7-3/4c=10

Solution for 3c+7-3/4c=10 equation:

3c+7-3/4c=10

We move all terms to the left:

3c+7-3/4c-(10)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R


We add all the numbers together, and all the variables

3c-3/4c-3=0

We multiply all the terms by the denominator


3c*4c-3*4c-3=0

Wy multiply elements

12c^2-12c-3=0

a = 12; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·12·(-3)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*12}=\frac{12-12\sqrt{2}}{24}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*12}=\frac{12+12\sqrt{2}}{24}
$