5(3x-7)(5x+4)=0

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Solution for 5(3x-7)(5x+4)=0 equation:



5(3x-7)(5x+4)=0
We multiply parentheses ..
5(+15x^2+12x-35x-28)=0
We multiply parentheses
75x^2+60x-175x-140=0
We add all the numbers together, and all the variables
75x^2-115x-140=0
a = 75; b = -115; c = -140;
Δ = b2-4ac
Δ = -1152-4·75·(-140)
Δ = 55225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{55225}=235$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-115)-235}{2*75}=\frac{-120}{150} =-4/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115)+235}{2*75}=\frac{350}{150} =2+1/3 $

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