(4x+7)(x-7)=0

Solution for (4x+7)(x-7)=0 equation:

(4x+7)(x-7)=0

We multiply parentheses ..

(+4x^2-28x+7x-49)=0

We get rid of parentheses

4x^2-28x+7x-49=0

We add all the numbers together, and all the variables

4x^2-21x-49=0

a = 4; b = -21; c = -49;
Δ = b2-4ac
Δ = -212-4·4·(-49)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-35}{2*4}=\frac{-14}{8}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+35}{2*4}=\frac{56}{8}
=7
$