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4x^2=27+12x
We move all terms to the left:
4x^2-(27+12x)=0
We add all the numbers together, and all the variables
4x^2-(12x+27)=0
We get rid of parentheses
4x^2-12x-27=0
a = 4; b = -12; c = -27;
Δ = b2-4ac
Δ = -122-4·4·(-27)
Δ = 576
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{576}=24$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*4}=\frac{-12}{8} =-1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*4}=\frac{36}{8} =4+1/2 $
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