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3-2x(x+4)=-13
We move all terms to the left:
3-2x(x+4)-(-13)=0
We add all the numbers together, and all the variables
-2x(x+4)+16=0
We multiply parentheses
-2x^2-8x+16=0
a = -2; b = -8; c = +16;
Δ = b2-4ac
Δ = -82-4·(-2)·16
Δ = 192
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{3}}{2*-2}=\frac{8-8\sqrt{3}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{3}}{2*-2}=\frac{8+8\sqrt{3}}{-4} $
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