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(3x-7)(x-5)=0
We multiply parentheses ..
(+3x^2-15x-7x+35)=0
We get rid of parentheses
3x^2-15x-7x+35=0
We add all the numbers together, and all the variables
3x^2-22x+35=0
a = 3; b = -22; c = +35;
Δ = b2-4ac
Δ = -222-4·3·35
Δ = 64
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{64}=8$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8}{2*3}=\frac{14}{6} =2+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8}{2*3}=\frac{30}{6} =5 $
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