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4.5x^2-19.5x+13=0
a = 4.5; b = -19.5; c = +13;
Δ = b2-4ac
Δ = -19.52-4·4.5·13
Δ = 146.25
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{-(-19.5)-\sqrt{146.25}}{2*4.5}=\frac{19.5-\sqrt{146.25}}{9} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19.5)+\sqrt{146.25}}{2*4.5}=\frac{19.5+\sqrt{146.25}}{9} $
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