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81x^2-90x+21=0
a = 81; b = -90; c = +21;
Δ = b2-4ac
Δ = -902-4·81·21
Δ = 1296
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{1296}=36$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-36}{2*81}=\frac{54}{162} =1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+36}{2*81}=\frac{126}{162} =7/9 $
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