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c^2+8c-27=23c-69
We move all terms to the left:
c^2+8c-27-(23c-69)=0
We get rid of parentheses
c^2+8c-23c+69-27=0
We add all the numbers together, and all the variables
c^2-15c+42=0
a = 1; b = -15; c = +42;
Δ = b2-4ac
Δ = -152-4·1·42
Δ = 57
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{-(-15)-\sqrt{57}}{2*1}=\frac{15-\sqrt{57}}{2} $$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{57}}{2*1}=\frac{15+\sqrt{57}}{2} $
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