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2x(x+8)-9=5
We move all terms to the left:
2x(x+8)-9-(5)=0
We add all the numbers together, and all the variables
2x(x+8)-14=0
We multiply parentheses
2x^2+16x-14=0
a = 2; b = 16; c = -14;
Δ = b2-4ac
Δ = 162-4·2·(-14)
Δ = 368
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{23}}{2*2}=\frac{-16-4\sqrt{23}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{23}}{2*2}=\frac{-16+4\sqrt{23}}{4} $
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