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4x^2+x-1/4=0
We multiply all the terms by the denominator
4x^2*4+x*4-1=0
Wy multiply elements
16x^2+4x-1=0
a = 16; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·16·(-1)
Δ = 80
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{5}}{2*16}=\frac{-4-4\sqrt{5}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{5}}{2*16}=\frac{-4+4\sqrt{5}}{32} $
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