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(6x+20)(4x+80)=180
We move all terms to the left:
(6x+20)(4x+80)-(180)=0
We multiply parentheses ..
(+24x^2+480x+80x+1600)-180=0
We get rid of parentheses
24x^2+480x+80x+1600-180=0
We add all the numbers together, and all the variables
24x^2+560x+1420=0
a = 24; b = 560; c = +1420;
Δ = b2-4ac
Δ = 5602-4·24·1420
Δ = 177280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{177280}=\sqrt{64*2770}=\sqrt{64}*\sqrt{2770}=8\sqrt{2770}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(560)-8\sqrt{2770}}{2*24}=\frac{-560-8\sqrt{2770}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(560)+8\sqrt{2770}}{2*24}=\frac{-560+8\sqrt{2770}}{48} $
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