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-7x(x+4)=14
We move all terms to the left:
-7x(x+4)-(14)=0
We multiply parentheses
-7x^2-28x-14=0
a = -7; b = -28; c = -14;
Δ = b2-4ac
Δ = -282-4·(-7)·(-14)
Δ = 392
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-14\sqrt{2}}{2*-7}=\frac{28-14\sqrt{2}}{-14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+14\sqrt{2}}{2*-7}=\frac{28+14\sqrt{2}}{-14} $
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