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(6x+11)(10x-9)=180
We move all terms to the left:
(6x+11)(10x-9)-(180)=0
We multiply parentheses ..
(+60x^2-54x+110x-99)-180=0
We get rid of parentheses
60x^2-54x+110x-99-180=0
We add all the numbers together, and all the variables
60x^2+56x-279=0
a = 60; b = 56; c = -279;
Δ = b2-4ac
Δ = 562-4·60·(-279)
Δ = 70096
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{70096}=\sqrt{16*4381}=\sqrt{16}*\sqrt{4381}=4\sqrt{4381}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{4381}}{2*60}=\frac{-56-4\sqrt{4381}}{120} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{4381}}{2*60}=\frac{-56+4\sqrt{4381}}{120} $
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