1/2c+10=5-7c

Solution for 1/2c+10=5-7c equation:

1/2c+10=5-7c

We move all terms to the left:

1/2c+10-(5-7c)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

1/2c-(-7c+5)+10=0

We get rid of parentheses

1/2c+7c-5+10=0

We multiply all the terms by the denominator


7c*2c-5*2c+10*2c+1=0

Wy multiply elements

14c^2-10c+20c+1=0

We add all the numbers together, and all the variables

14c^2+10c+1=0

a = 14; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·14·1
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{11}}{2*14}=\frac{-10-2\sqrt{11}}{28}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{11}}{2*14}=\frac{-10+2\sqrt{11}}{28}
$