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9x^2+8x-52=0
a = 9; b = 8; c = -52;
Δ = b2-4ac
Δ = 82-4·9·(-52)
Δ = 1936
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{1936}=44$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-44}{2*9}=\frac{-52}{18} =-2+8/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+44}{2*9}=\frac{36}{18} =2 $
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