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4x(x-7)=14
We move all terms to the left:
4x(x-7)-(14)=0
We multiply parentheses
4x^2-28x-14=0
a = 4; b = -28; c = -14;
Δ = b2-4ac
Δ = -282-4·4·(-14)
Δ = 1008
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-12\sqrt{7}}{2*4}=\frac{28-12\sqrt{7}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+12\sqrt{7}}{2*4}=\frac{28+12\sqrt{7}}{8} $
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