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65x^2-64x+15=0
a = 65; b = -64; c = +15;
Δ = b2-4ac
Δ = -642-4·65·15
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-14}{2*65}=\frac{50}{130} =5/13 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+14}{2*65}=\frac{78}{130} =3/5 $
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