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(3x-5)(8x-2)=0
We multiply parentheses ..
(+24x^2-6x-40x+10)=0
We get rid of parentheses
24x^2-6x-40x+10=0
We add all the numbers together, and all the variables
24x^2-46x+10=0
a = 24; b = -46; c = +10;
Δ = b2-4ac
Δ = -462-4·24·10
Δ = 1156
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{1156}=34$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-34}{2*24}=\frac{12}{48} =1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+34}{2*24}=\frac{80}{48} =1+2/3 $
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