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a^2+27=2a^2-54
We move all terms to the left:
a^2+27-(2a^2-54)=0
We get rid of parentheses
a^2-2a^2+54+27=0
We add all the numbers together, and all the variables
-1a^2+81=0
a = -1; b = 0; c = +81;
Δ = b2-4ac
Δ = 02-4·(-1)·81
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{324}=18$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*-1}=\frac{-18}{-2} =+9 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*-1}=\frac{18}{-2} =-9 $
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