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(5x-27)(3x-1)=180
We move all terms to the left:
(5x-27)(3x-1)-(180)=0
We multiply parentheses ..
(+15x^2-5x-81x+27)-180=0
We get rid of parentheses
15x^2-5x-81x+27-180=0
We add all the numbers together, and all the variables
15x^2-86x-153=0
a = 15; b = -86; c = -153;
Δ = b2-4ac
Δ = -862-4·15·(-153)
Δ = 16576
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16576}=\sqrt{64*259}=\sqrt{64}*\sqrt{259}=8\sqrt{259}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-8\sqrt{259}}{2*15}=\frac{86-8\sqrt{259}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+8\sqrt{259}}{2*15}=\frac{86+8\sqrt{259}}{30} $
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