4/10c-4+2c-7=20

Solution for 4/10c-4+2c-7=20 equation:

4/10c-4+2c-7=20

We move all terms to the left:

4/10c-4+2c-7-(20)=0


Domain of the equation: 10c!=0

c!=0/10

c!=0

c∈R


We add all the numbers together, and all the variables

2c+4/10c-31=0

We multiply all the terms by the denominator


2c*10c-31*10c+4=0

Wy multiply elements

20c^2-310c+4=0

a = 20; b = -310; c = +4;
Δ = b2-4ac
Δ = -3102-4·20·4
Δ = 95780
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:

$\sqrt{\Delta}=\sqrt{95780}=\sqrt{4*23945}=\sqrt{4}*\sqrt{23945}=2\sqrt{23945}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-310)-2\sqrt{23945}}{2*20}=\frac{310-2\sqrt{23945}}{40}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-310)+2\sqrt{23945}}{2*20}=\frac{310+2\sqrt{23945}}{40}
$