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3.4x^2-8.1x+1=0
a = 3.4; b = -8.1; c = +1;
Δ = b2-4ac
Δ = -8.12-4·3.4·1
Δ = 52.01
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8.1)-\sqrt{52.01}}{2*3.4}=\frac{8.1-\sqrt{52.01}}{6.8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.1)+\sqrt{52.01}}{2*3.4}=\frac{8.1+\sqrt{52.01}}{6.8} $
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