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(2x+1)(5x-9)=0
We multiply parentheses ..
(+10x^2-18x+5x-9)=0
We get rid of parentheses
10x^2-18x+5x-9=0
We add all the numbers together, and all the variables
10x^2-13x-9=0
a = 10; b = -13; c = -9;
Δ = b2-4ac
Δ = -132-4·10·(-9)
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*10}=\frac{-10}{20} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*10}=\frac{36}{20} =1+4/5 $
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