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(2x-3)(5x-3)=0
We multiply parentheses ..
(+10x^2-6x-15x+9)=0
We get rid of parentheses
10x^2-6x-15x+9=0
We add all the numbers together, and all the variables
10x^2-21x+9=0
a = 10; b = -21; c = +9;
Δ = b2-4ac
Δ = -212-4·10·9
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9}{2*10}=\frac{12}{20} =3/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*10}=\frac{30}{20} =1+1/2 $
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