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7x^2-x-19=0
We add all the numbers together, and all the variables
7x^2-1x-19=0
a = 7; b = -1; c = -19;
Δ = b2-4ac
Δ = -12-4·7·(-19)
Δ = 533
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{533}}{2*7}=\frac{1-\sqrt{533}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{533}}{2*7}=\frac{1+\sqrt{533}}{14} $
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