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(4x-1)(3x-10)=0
We multiply parentheses ..
(+12x^2-40x-3x+10)=0
We get rid of parentheses
12x^2-40x-3x+10=0
We add all the numbers together, and all the variables
12x^2-43x+10=0
a = 12; b = -43; c = +10;
Δ = b2-4ac
Δ = -432-4·12·10
Δ = 1369
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{1369}=37$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-37}{2*12}=\frac{6}{24} =1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+37}{2*12}=\frac{80}{24} =3+1/3 $
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