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4x^2+17x+17=1
We move all terms to the left:
4x^2+17x+17-(1)=0
We add all the numbers together, and all the variables
4x^2+17x+16=0
a = 4; b = 17; c = +16;
Δ = b2-4ac
Δ = 172-4·4·16
Δ = 33
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{-(17)-\sqrt{33}}{2*4}=\frac{-17-\sqrt{33}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{33}}{2*4}=\frac{-17+\sqrt{33}}{8} $
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