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90+(5x+9)(4x+27)=180
We move all terms to the left:
90+(5x+9)(4x+27)-(180)=0
We add all the numbers together, and all the variables
(5x+9)(4x+27)-90=0
We multiply parentheses ..
(+20x^2+135x+36x+243)-90=0
We get rid of parentheses
20x^2+135x+36x+243-90=0
We add all the numbers together, and all the variables
20x^2+171x+153=0
a = 20; b = 171; c = +153;
Δ = b2-4ac
Δ = 1712-4·20·153
Δ = 17001
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17001}=\sqrt{9*1889}=\sqrt{9}*\sqrt{1889}=3\sqrt{1889}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(171)-3\sqrt{1889}}{2*20}=\frac{-171-3\sqrt{1889}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(171)+3\sqrt{1889}}{2*20}=\frac{-171+3\sqrt{1889}}{40} $
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