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(84-2x)(93-3x)=180
We move all terms to the left:
(84-2x)(93-3x)-(180)=0
We add all the numbers together, and all the variables
(-2x+84)(-3x+93)-180=0
We multiply parentheses ..
(+6x^2-186x-252x+7812)-180=0
We get rid of parentheses
6x^2-186x-252x+7812-180=0
We add all the numbers together, and all the variables
6x^2-438x+7632=0
a = 6; b = -438; c = +7632;
Δ = b2-4ac
Δ = -4382-4·6·7632
Δ = 8676
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8676}=\sqrt{36*241}=\sqrt{36}*\sqrt{241}=6\sqrt{241}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-438)-6\sqrt{241}}{2*6}=\frac{438-6\sqrt{241}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-438)+6\sqrt{241}}{2*6}=\frac{438+6\sqrt{241}}{12} $
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