(7x+2)(5x-3)=0

Solution for (7x+2)(5x-3)=0 equation:

(7x+2)(5x-3)=0

We multiply parentheses ..

(+35x^2-21x+10x-6)=0

We get rid of parentheses

35x^2-21x+10x-6=0

We add all the numbers together, and all the variables

35x^2-11x-6=0

a = 35; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·35·(-6)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-31}{2*35}=\frac{-20}{70}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*35}=\frac{42}{70}
=3/5
$