(7x-6)(10x+7)=0

Solution for (7x-6)(10x+7)=0 equation:

(7x-6)(10x+7)=0

We multiply parentheses ..

(+70x^2+49x-60x-42)=0

We get rid of parentheses

70x^2+49x-60x-42=0

We add all the numbers together, and all the variables

70x^2-11x-42=0

a = 70; b = -11; c = -42;
Δ = b2-4ac
Δ = -112-4·70·(-42)
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-109}{2*70}=\frac{-98}{140}
=-7/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+109}{2*70}=\frac{120}{140}
=6/7
$