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-6x+54=4x^2
We move all terms to the left:
-6x+54-(4x^2)=0
determiningTheFunctionDomain -4x^2-6x+54=0
a = -4; b = -6; c = +54;
Δ = b2-4ac
Δ = -62-4·(-4)·54
Δ = 900
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{900}=30$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*-4}=\frac{-24}{-8} =+3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*-4}=\frac{36}{-8} =-4+1/2 $
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