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4a^2-31a-90=0
a = 4; b = -31; c = -90;
Δ = b2-4ac
Δ = -312-4·4·(-90)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2401}=49$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-49}{2*4}=\frac{-18}{8} =-2+1/4 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+49}{2*4}=\frac{80}{8} =10 $
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