(13x+7)(6x-7)=0

Solution for (13x+7)(6x-7)=0 equation:

(13x+7)(6x-7)=0

We multiply parentheses ..

(+78x^2-91x+42x-49)=0

We get rid of parentheses

78x^2-91x+42x-49=0

We add all the numbers together, and all the variables

78x^2-49x-49=0

a = 78; b = -49; c = -49;
Δ = b2-4ac
Δ = -492-4·78·(-49)
Δ = 17689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17689}=133$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-133}{2*78}=\frac{-84}{156}
=-7/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+133}{2*78}=\frac{182}{156}
=1+1/6
$