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X=6-2.7X^2
We move all terms to the left:
X-(6-2.7X^2)=0
We get rid of parentheses
2.7X^2+X-6=0
a = 2.7; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·2.7·(-6)
Δ = 65.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{65.8}}{2*2.7}=\frac{-1-\sqrt{65.8}}{5.4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{65.8}}{2*2.7}=\frac{-1+\sqrt{65.8}}{5.4} $
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