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7(2x^2-3)=x
We move all terms to the left:
7(2x^2-3)-(x)=0
We add all the numbers together, and all the variables
-1x+7(2x^2-3)=0
We multiply parentheses
14x^2-1x-21=0
a = 14; b = -1; c = -21;
Δ = b2-4ac
Δ = -12-4·14·(-21)
Δ = 1177
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{1177}}{2*14}=\frac{1-\sqrt{1177}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1177}}{2*14}=\frac{1+\sqrt{1177}}{28} $
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