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4x^2-x=6
We move all terms to the left:
4x^2-x-(6)=0
We add all the numbers together, and all the variables
4x^2-1x-6=0
a = 4; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·4·(-6)
Δ = 97
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{-(-1)-\sqrt{97}}{2*4}=\frac{1-\sqrt{97}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*4}=\frac{1+\sqrt{97}}{8} $
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