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(3x-1)(2x-6)=135
We move all terms to the left:
(3x-1)(2x-6)-(135)=0
We multiply parentheses ..
(+6x^2-18x-2x+6)-135=0
We get rid of parentheses
6x^2-18x-2x+6-135=0
We add all the numbers together, and all the variables
6x^2-20x-129=0
a = 6; b = -20; c = -129;
Δ = b2-4ac
Δ = -202-4·6·(-129)
Δ = 3496
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3496}=\sqrt{4*874}=\sqrt{4}*\sqrt{874}=2\sqrt{874}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{874}}{2*6}=\frac{20-2\sqrt{874}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{874}}{2*6}=\frac{20+2\sqrt{874}}{12} $
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