(2x-7)(8x+7)=0

Solution for (2x-7)(8x+7)=0 equation:

(2x-7)(8x+7)=0

We multiply parentheses ..

(+16x^2+14x-56x-49)=0

We get rid of parentheses

16x^2+14x-56x-49=0

We add all the numbers together, and all the variables

16x^2-42x-49=0

a = 16; b = -42; c = -49;
Δ = b2-4ac
Δ = -422-4·16·(-49)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-70}{2*16}=\frac{-28}{32}
=-7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+70}{2*16}=\frac{112}{32}
=3+1/2
$