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4x^2-21x+27=0
a = 4; b = -21; c = +27;
Δ = b2-4ac
Δ = -212-4·4·27
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*4}=\frac{18}{8} =2+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*4}=\frac{24}{8} =3 $
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