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(9x-2)(5x-8)=0
We multiply parentheses ..
(+45x^2-72x-10x+16)=0
We get rid of parentheses
45x^2-72x-10x+16=0
We add all the numbers together, and all the variables
45x^2-82x+16=0
a = 45; b = -82; c = +16;
Δ = b2-4ac
Δ = -822-4·45·16
Δ = 3844
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{3844}=62$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-62}{2*45}=\frac{20}{90} =2/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+62}{2*45}=\frac{144}{90} =1+3/5 $
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