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5(x-3)(x-8)=0
We multiply parentheses ..
5(+x^2-8x-3x+24)=0
We multiply parentheses
5x^2-40x-15x+120=0
We add all the numbers together, and all the variables
5x^2-55x+120=0
a = 5; b = -55; c = +120;
Δ = b2-4ac
Δ = -552-4·5·120
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-25}{2*5}=\frac{30}{10} =3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+25}{2*5}=\frac{80}{10} =8 $
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