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2x(4x-1)=50
We move all terms to the left:
2x(4x-1)-(50)=0
We multiply parentheses
8x^2-2x-50=0
a = 8; b = -2; c = -50;
Δ = b2-4ac
Δ = -22-4·8·(-50)
Δ = 1604
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1604}=\sqrt{4*401}=\sqrt{4}*\sqrt{401}=2\sqrt{401}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{401}}{2*8}=\frac{2-2\sqrt{401}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{401}}{2*8}=\frac{2+2\sqrt{401}}{16} $
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