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-13.72x^2+23.52x-10=0
a = -13.72; b = 23.52; c = -10;
Δ = b2-4ac
Δ = 23.522-4·(-13.72)·(-10)
Δ = 4.3904
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{-(23.52)-\sqrt{4.3904}}{2*-13.72}=\frac{-23.52-\sqrt{4.3904}}{-27.44} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23.52)+\sqrt{4.3904}}{2*-13.72}=\frac{-23.52+\sqrt{4.3904}}{-27.44} $
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