(5x-9)(7x+6)=0

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Solution for (5x-9)(7x+6)=0 equation:



(5x-9)(7x+6)=0
We multiply parentheses ..
(+35x^2+30x-63x-54)=0
We get rid of parentheses
35x^2+30x-63x-54=0
We add all the numbers together, and all the variables
35x^2-33x-54=0
a = 35; b = -33; c = -54;
Δ = b2-4ac
Δ = -332-4·35·(-54)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-93}{2*35}=\frac{-60}{70} =-6/7 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+93}{2*35}=\frac{126}{70} =1+4/5 $

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