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2c+6+1/2c+5+3c+4=180
We move all terms to the left:
2c+6+1/2c+5+3c+4-(180)=0
Domain of the equation: 2c!=0We add all the numbers together, and all the variables
c!=0/2
c!=0
c∈R
5c+1/2c-165=0
We multiply all the terms by the denominator
5c*2c-165*2c+1=0
Wy multiply elements
10c^2-330c+1=0
a = 10; b = -330; c = +1;
Δ = b2-4ac
Δ = -3302-4·10·1
Δ = 108860
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}$$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{108860}=\sqrt{4*27215}=\sqrt{4}*\sqrt{27215}=2\sqrt{27215}$$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-2\sqrt{27215}}{2*10}=\frac{330-2\sqrt{27215}}{20} $$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+2\sqrt{27215}}{2*10}=\frac{330+2\sqrt{27215}}{20} $
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