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

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

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

We multiply parentheses ..

5(+21x^2+9x-35x-15)=0

We multiply parentheses

105x^2+45x-175x-75=0

We add all the numbers together, and all the variables

105x^2-130x-75=0

a = 105; b = -130; c = -75;
Δ = b2-4ac
Δ = -1302-4·105·(-75)
Δ = 48400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{48400}=220$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-220}{2*105}=\frac{-90}{210}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+220}{2*105}=\frac{350}{210}
=1+2/3
$