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0.35x^2+5.3x-117.66=0
a = 0.35; b = 5.3; c = -117.66;
Δ = b2-4ac
Δ = 5.32-4·0.35·(-117.66)
Δ = 192.814
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{-(5.3)-\sqrt{192.814}}{2*0.35}=\frac{-5.3-\sqrt{192.814}}{0.7} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.3)+\sqrt{192.814}}{2*0.35}=\frac{-5.3+\sqrt{192.814}}{0.7} $
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