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(4x-5)(2x-1)=0
We multiply parentheses ..
(+8x^2-4x-10x+5)=0
We get rid of parentheses
8x^2-4x-10x+5=0
We add all the numbers together, and all the variables
8x^2-14x+5=0
a = 8; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·8·5
Δ = 36
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{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*8}=\frac{8}{16} =1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*8}=\frac{20}{16} =1+1/4 $
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