(7x-15)(3x+19)=0

Solution for (7x-15)(3x+19)=0 equation:

(7x-15)(3x+19)=0

We multiply parentheses ..

(+21x^2+133x-45x-285)=0

We get rid of parentheses

21x^2+133x-45x-285=0

We add all the numbers together, and all the variables

21x^2+88x-285=0

a = 21; b = 88; c = -285;
Δ = b2-4ac
Δ = 882-4·21·(-285)
Δ = 31684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{31684}=178$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-178}{2*21}=\frac{-266}{42}
=-6+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+178}{2*21}=\frac{90}{42}
=2+1/7
$