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(3x+20)(+2x+80)=180
We move all terms to the left:
(3x+20)(+2x+80)-(180)=0
We add all the numbers together, and all the variables
(3x+20)(2x+80)-180=0
We multiply parentheses ..
(+6x^2+240x+40x+1600)-180=0
We get rid of parentheses
6x^2+240x+40x+1600-180=0
We add all the numbers together, and all the variables
6x^2+280x+1420=0
a = 6; b = 280; c = +1420;
Δ = b2-4ac
Δ = 2802-4·6·1420
Δ = 44320
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44320}=\sqrt{16*2770}=\sqrt{16}*\sqrt{2770}=4\sqrt{2770}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-4\sqrt{2770}}{2*6}=\frac{-280-4\sqrt{2770}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+4\sqrt{2770}}{2*6}=\frac{-280+4\sqrt{2770}}{12} $
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