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2a^2=27-15a
We move all terms to the left:
2a^2-(27-15a)=0
We add all the numbers together, and all the variables
2a^2-(-15a+27)=0
We get rid of parentheses
2a^2+15a-27=0
a = 2; b = 15; c = -27;
Δ = b2-4ac
Δ = 152-4·2·(-27)
Δ = 441
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{441}=21$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*2}=\frac{-36}{4} =-9 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*2}=\frac{6}{4} =1+1/2 $
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