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4x^2-27x=-18
We move all terms to the left:
4x^2-27x-(-18)=0
We add all the numbers together, and all the variables
4x^2-27x+18=0
a = 4; b = -27; c = +18;
Δ = b2-4ac
Δ = -272-4·4·18
Δ = 441
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{441}=21$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-21}{2*4}=\frac{6}{8} =3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+21}{2*4}=\frac{48}{8} =6 $
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