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2x(2x+4)=14
We move all terms to the left:
2x(2x+4)-(14)=0
We multiply parentheses
4x^2+8x-14=0
a = 4; b = 8; c = -14;
Δ = b2-4ac
Δ = 82-4·4·(-14)
Δ = 288
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{2}}{2*4}=\frac{-8-12\sqrt{2}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{2}}{2*4}=\frac{-8+12\sqrt{2}}{8} $
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