(5x-2)(7x+6)=0

Solution for (5x-2)(7x+6)=0 equation:

(5x-2)(7x+6)=0

We multiply parentheses ..

(+35x^2+30x-14x-12)=0

We get rid of parentheses

35x^2+30x-14x-12=0

We add all the numbers together, and all the variables

35x^2+16x-12=0

a = 35; b = 16; c = -12;
Δ = b2-4ac
Δ = 162-4·35·(-12)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-44}{2*35}=\frac{-60}{70}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+44}{2*35}=\frac{28}{70}
=2/5
$