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2x^2+25x-8.5=0
a = 2; b = 25; c = -8.5;
Δ = b2-4ac
Δ = 252-4·2·(-8.5)
Δ = 693
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{693}=\sqrt{9*77}=\sqrt{9}*\sqrt{77}=3\sqrt{77}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-3\sqrt{77}}{2*2}=\frac{-25-3\sqrt{77}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+3\sqrt{77}}{2*2}=\frac{-25+3\sqrt{77}}{4} $
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