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2x(7x+1)=254
We move all terms to the left:
2x(7x+1)-(254)=0
We multiply parentheses
14x^2+2x-254=0
a = 14; b = 2; c = -254;
Δ = b2-4ac
Δ = 22-4·14·(-254)
Δ = 14228
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14228}=\sqrt{4*3557}=\sqrt{4}*\sqrt{3557}=2\sqrt{3557}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3557}}{2*14}=\frac{-2-2\sqrt{3557}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3557}}{2*14}=\frac{-2+2\sqrt{3557}}{28} $
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