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14x(6x-24)=5x-7
We move all terms to the left:
14x(6x-24)-(5x-7)=0
We multiply parentheses
84x^2-336x-(5x-7)=0
We get rid of parentheses
84x^2-336x-5x+7=0
We add all the numbers together, and all the variables
84x^2-341x+7=0
a = 84; b = -341; c = +7;
Δ = b2-4ac
Δ = -3412-4·84·7
Δ = 113929
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{-(-341)-\sqrt{113929}}{2*84}=\frac{341-\sqrt{113929}}{168} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-341)+\sqrt{113929}}{2*84}=\frac{341+\sqrt{113929}}{168} $
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