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9x^2-61x+52=0
a = 9; b = -61; c = +52;
Δ = b2-4ac
Δ = -612-4·9·52
Δ = 1849
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{1849}=43$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-43}{2*9}=\frac{18}{18} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+43}{2*9}=\frac{104}{18} =5+7/9 $
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