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(10x-7)(3x-1)=0
We multiply parentheses ..
(+30x^2-10x-21x+7)=0
We get rid of parentheses
30x^2-10x-21x+7=0
We add all the numbers together, and all the variables
30x^2-31x+7=0
a = 30; b = -31; c = +7;
Δ = b2-4ac
Δ = -312-4·30·7
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-11}{2*30}=\frac{20}{60} =1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+11}{2*30}=\frac{42}{60} =7/10 $
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