-7(x+5)(x-12)=0

Solution for -7(x+5)(x-12)=0 equation:

-7(x+5)(x-12)=0

We multiply parentheses ..

-7(+x^2-12x+5x-60)=0

We multiply parentheses

-7x^2+84x-35x+420=0

We add all the numbers together, and all the variables

-7x^2+49x+420=0

a = -7; b = 49; c = +420;
Δ = b2-4ac
Δ = 492-4·(-7)·420
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-119}{2*-7}=\frac{-168}{-14}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+119}{2*-7}=\frac{70}{-14}
=-5
$