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(5x-3)(2x-9)=0
We multiply parentheses ..
(+10x^2-45x-6x+27)=0
We get rid of parentheses
10x^2-45x-6x+27=0
We add all the numbers together, and all the variables
10x^2-51x+27=0
a = 10; b = -51; c = +27;
Δ = b2-4ac
Δ = -512-4·10·27
Δ = 1521
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{1521}=39$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-39}{2*10}=\frac{12}{20} =3/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+39}{2*10}=\frac{90}{20} =4+1/2 $
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