(5x-3)(7x+6)=0

Solution for (5x-3)(7x+6)=0 equation:

(5x-3)(7x+6)=0

We multiply parentheses ..

(+35x^2+30x-21x-18)=0

We get rid of parentheses

35x^2+30x-21x-18=0

We add all the numbers together, and all the variables

35x^2+9x-18=0

a = 35; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·35·(-18)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-51}{2*35}=\frac{-60}{70}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+51}{2*35}=\frac{42}{70}
=3/5
$