(7x-2)(x-7)=0

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Solution for (7x-2)(x-7)=0 equation:



(7x-2)(x-7)=0
We multiply parentheses ..
(+7x^2-49x-2x+14)=0
We get rid of parentheses
7x^2-49x-2x+14=0
We add all the numbers together, and all the variables
7x^2-51x+14=0
a = 7; b = -51; c = +14;
Δ = b2-4ac
Δ = -512-4·7·14
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-47}{2*7}=\frac{4}{14} =2/7 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+47}{2*7}=\frac{98}{14} =7 $

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