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4x^2-x-3=x
We move all terms to the left:
4x^2-x-3-(x)=0
We add all the numbers together, and all the variables
4x^2-2x-3=0
a = 4; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·4·(-3)
Δ = 52
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*4}=\frac{2-2\sqrt{13}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*4}=\frac{2+2\sqrt{13}}{8} $
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