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

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



(3x+7)(-5x+3)=0
We multiply parentheses ..
(-15x^2+9x-35x+21)=0
We get rid of parentheses
-15x^2+9x-35x+21=0
We add all the numbers together, and all the variables
-15x^2-26x+21=0
a = -15; b = -26; c = +21;
Δ = b2-4ac
Δ = -262-4·(-15)·21
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-44}{2*-15}=\frac{-18}{-30} =3/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+44}{2*-15}=\frac{70}{-30} =-2+1/3 $

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