(2x-9)(7x+7)=0

Solution for (2x-9)(7x+7)=0 equation:

(2x-9)(7x+7)=0

We multiply parentheses ..

(+14x^2+14x-63x-63)=0

We get rid of parentheses

14x^2+14x-63x-63=0

We add all the numbers together, and all the variables

14x^2-49x-63=0

a = 14; b = -49; c = -63;
Δ = b2-4ac
Δ = -492-4·14·(-63)
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-77}{2*14}=\frac{-28}{28}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+77}{2*14}=\frac{126}{28}
=4+1/2
$