7(x-6)(2x+9)=0

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Solution for 7(x-6)(2x+9)=0 equation:



7(x-6)(2x+9)=0
We multiply parentheses ..
7(+2x^2+9x-12x-54)=0
We multiply parentheses
14x^2+63x-84x-378=0
We add all the numbers together, and all the variables
14x^2-21x-378=0
a = 14; b = -21; c = -378;
Δ = b2-4ac
Δ = -212-4·14·(-378)
Δ = 21609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21609}=147$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-147}{2*14}=\frac{-126}{28} =-4+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+147}{2*14}=\frac{168}{28} =6 $

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