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4x(x+7)+9=23
We move all terms to the left:
4x(x+7)+9-(23)=0
We add all the numbers together, and all the variables
4x(x+7)-14=0
We multiply parentheses
4x^2+28x-14=0
a = 4; b = 28; c = -14;
Δ = b2-4ac
Δ = 282-4·4·(-14)
Δ = 1008
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12\sqrt{7}}{2*4}=\frac{-28-12\sqrt{7}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12\sqrt{7}}{2*4}=\frac{-28+12\sqrt{7}}{8} $
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