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(9x+4)(4x+1)+83=180
We move all terms to the left:
(9x+4)(4x+1)+83-(180)=0
We add all the numbers together, and all the variables
(9x+4)(4x+1)-97=0
We multiply parentheses ..
(+36x^2+9x+16x+4)-97=0
We get rid of parentheses
36x^2+9x+16x+4-97=0
We add all the numbers together, and all the variables
36x^2+25x-93=0
a = 36; b = 25; c = -93;
Δ = b2-4ac
Δ = 252-4·36·(-93)
Δ = 14017
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{14017}}{2*36}=\frac{-25-\sqrt{14017}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{14017}}{2*36}=\frac{-25+\sqrt{14017}}{72} $
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