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(4x+9)4x=144
We move all terms to the left:
(4x+9)4x-(144)=0
We multiply parentheses
16x^2+36x-144=0
a = 16; b = 36; c = -144;
Δ = b2-4ac
Δ = 362-4·16·(-144)
Δ = 10512
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10512}=\sqrt{144*73}=\sqrt{144}*\sqrt{73}=12\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{73}}{2*16}=\frac{-36-12\sqrt{73}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{73}}{2*16}=\frac{-36+12\sqrt{73}}{32} $
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