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(5x-3)(5x-8)=0
We multiply parentheses ..
(+25x^2-40x-15x+24)=0
We get rid of parentheses
25x^2-40x-15x+24=0
We add all the numbers together, and all the variables
25x^2-55x+24=0
a = 25; b = -55; c = +24;
Δ = b2-4ac
Δ = -552-4·25·24
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-25}{2*25}=\frac{30}{50} =3/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+25}{2*25}=\frac{80}{50} =1+3/5 $
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