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(6c-4)-(c-3)c=7
We move all terms to the left:
(6c-4)-(c-3)c-(7)=0
We multiply parentheses
-c^2+(6c-4)+3c-7=0
We get rid of parentheses
-c^2+6c+3c-4-7=0
We add all the numbers together, and all the variables
-1c^2+9c-11=0
a = -1; b = 9; c = -11;
Δ = b2-4ac
Δ = 92-4·(-1)·(-11)
Δ = 37
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}$$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{37}}{2*-1}=\frac{-9-\sqrt{37}}{-2} $$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{37}}{2*-1}=\frac{-9+\sqrt{37}}{-2} $
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