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(6x+1)(4x-6)45=180
We move all terms to the left:
(6x+1)(4x-6)45-(180)=0
We multiply parentheses ..
(+24x^2-36x+4x-6)45-180=0
We multiply parentheses
1080x^2-1620x+180x-270-180=0
We add all the numbers together, and all the variables
1080x^2-1440x-450=0
a = 1080; b = -1440; c = -450;
Δ = b2-4ac
Δ = -14402-4·1080·(-450)
Δ = 4017600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4017600}=\sqrt{129600*31}=\sqrt{129600}*\sqrt{31}=360\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1440)-360\sqrt{31}}{2*1080}=\frac{1440-360\sqrt{31}}{2160} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1440)+360\sqrt{31}}{2*1080}=\frac{1440+360\sqrt{31}}{2160} $
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