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(5x-54)(3x+16)=0
We multiply parentheses ..
(+15x^2+80x-162x-864)=0
We get rid of parentheses
15x^2+80x-162x-864=0
We add all the numbers together, and all the variables
15x^2-82x-864=0
a = 15; b = -82; c = -864;
Δ = b2-4ac
Δ = -822-4·15·(-864)
Δ = 58564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{58564}=242$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-242}{2*15}=\frac{-160}{30} =-5+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+242}{2*15}=\frac{324}{30} =10+4/5 $
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