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7(2x^2-1)=5x
We move all terms to the left:
7(2x^2-1)-(5x)=0
We add all the numbers together, and all the variables
-5x+7(2x^2-1)=0
We multiply parentheses
14x^2-5x-7=0
a = 14; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·14·(-7)
Δ = 417
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{-(-5)-\sqrt{417}}{2*14}=\frac{5-\sqrt{417}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{417}}{2*14}=\frac{5+\sqrt{417}}{28} $
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