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(3x+20)(5x-16)=180
We move all terms to the left:
(3x+20)(5x-16)-(180)=0
We multiply parentheses ..
(+15x^2-48x+100x-320)-180=0
We get rid of parentheses
15x^2-48x+100x-320-180=0
We add all the numbers together, and all the variables
15x^2+52x-500=0
a = 15; b = 52; c = -500;
Δ = b2-4ac
Δ = 522-4·15·(-500)
Δ = 32704
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32704}=\sqrt{64*511}=\sqrt{64}*\sqrt{511}=8\sqrt{511}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-8\sqrt{511}}{2*15}=\frac{-52-8\sqrt{511}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+8\sqrt{511}}{2*15}=\frac{-52+8\sqrt{511}}{30} $
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