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(2x-24)(5x-27)=180
We move all terms to the left:
(2x-24)(5x-27)-(180)=0
We multiply parentheses ..
(+10x^2-54x-120x+648)-180=0
We get rid of parentheses
10x^2-54x-120x+648-180=0
We add all the numbers together, and all the variables
10x^2-174x+468=0
a = 10; b = -174; c = +468;
Δ = b2-4ac
Δ = -1742-4·10·468
Δ = 11556
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11556}=\sqrt{36*321}=\sqrt{36}*\sqrt{321}=6\sqrt{321}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-174)-6\sqrt{321}}{2*10}=\frac{174-6\sqrt{321}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-174)+6\sqrt{321}}{2*10}=\frac{174+6\sqrt{321}}{20} $
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