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(2x+60)(3x-40)=180
We move all terms to the left:
(2x+60)(3x-40)-(180)=0
We multiply parentheses ..
(+6x^2-80x+180x-2400)-180=0
We get rid of parentheses
6x^2-80x+180x-2400-180=0
We add all the numbers together, and all the variables
6x^2+100x-2580=0
a = 6; b = 100; c = -2580;
Δ = b2-4ac
Δ = 1002-4·6·(-2580)
Δ = 71920
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{71920}=\sqrt{16*4495}=\sqrt{16}*\sqrt{4495}=4\sqrt{4495}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{4495}}{2*6}=\frac{-100-4\sqrt{4495}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{4495}}{2*6}=\frac{-100+4\sqrt{4495}}{12} $
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