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8x(x+2)=2x+16
We move all terms to the left:
8x(x+2)-(2x+16)=0
We multiply parentheses
8x^2+16x-(2x+16)=0
We get rid of parentheses
8x^2+16x-2x-16=0
We add all the numbers together, and all the variables
8x^2+14x-16=0
a = 8; b = 14; c = -16;
Δ = b2-4ac
Δ = 142-4·8·(-16)
Δ = 708
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{177}}{2*8}=\frac{-14-2\sqrt{177}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{177}}{2*8}=\frac{-14+2\sqrt{177}}{16} $
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