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7x^2-5x-32=0
a = 7; b = -5; c = -32;
Δ = b2-4ac
Δ = -52-4·7·(-32)
Δ = 921
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{-(-5)-\sqrt{921}}{2*7}=\frac{5-\sqrt{921}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{921}}{2*7}=\frac{5+\sqrt{921}}{14} $
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