7(x+5)(3x-1)=0

Solution for 7(x+5)(3x-1)=0 equation:

7(x+5)(3x-1)=0

We multiply parentheses ..

7(+3x^2-1x+15x-5)=0

We multiply parentheses

21x^2-7x+105x-35=0

We add all the numbers together, and all the variables

21x^2+98x-35=0

a = 21; b = 98; c = -35;
Δ = b2-4ac
Δ = 982-4·21·(-35)
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-112}{2*21}=\frac{-210}{42}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+112}{2*21}=\frac{14}{42}
=1/3
$