(3x-7)(2x-8)=0

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Solution for (3x-7)(2x-8)=0 equation:



(3x-7)(2x-8)=0
We multiply parentheses ..
(+6x^2-24x-14x+56)=0
We get rid of parentheses
6x^2-24x-14x+56=0
We add all the numbers together, and all the variables
6x^2-38x+56=0
a = 6; b = -38; c = +56;
Δ = b2-4ac
Δ = -382-4·6·56
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-10}{2*6}=\frac{28}{12} =2+1/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+10}{2*6}=\frac{48}{12} =4 $

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