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(9x+1)(13x-11)=180
We move all terms to the left:
(9x+1)(13x-11)-(180)=0
We multiply parentheses ..
(+117x^2-99x+13x-11)-180=0
We get rid of parentheses
117x^2-99x+13x-11-180=0
We add all the numbers together, and all the variables
117x^2-86x-191=0
a = 117; b = -86; c = -191;
Δ = b2-4ac
Δ = -862-4·117·(-191)
Δ = 96784
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{96784}=\sqrt{16*6049}=\sqrt{16}*\sqrt{6049}=4\sqrt{6049}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-4\sqrt{6049}}{2*117}=\frac{86-4\sqrt{6049}}{234} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+4\sqrt{6049}}{2*117}=\frac{86+4\sqrt{6049}}{234} $
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