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2b^2-11b-15=0
a = 2; b = -11; c = -15;
Δ = b2-4ac
Δ = -112-4·2·(-15)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{241}}{2*2}=\frac{11-\sqrt{241}}{4} $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{241}}{2*2}=\frac{11+\sqrt{241}}{4} $
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