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(7x-1)(2x-5)=0
We multiply parentheses ..
(+14x^2-35x-2x+5)=0
We get rid of parentheses
14x^2-35x-2x+5=0
We add all the numbers together, and all the variables
14x^2-37x+5=0
a = 14; b = -37; c = +5;
Δ = b2-4ac
Δ = -372-4·14·5
Δ = 1089
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{1089}=33$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-33}{2*14}=\frac{4}{28} =1/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+33}{2*14}=\frac{70}{28} =2+1/2 $
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