(4x-7)(2x+6)=0

Solution for (4x-7)(2x+6)=0 equation:

(4x-7)(2x+6)=0

We multiply parentheses ..

(+8x^2+24x-14x-42)=0

We get rid of parentheses

8x^2+24x-14x-42=0

We add all the numbers together, and all the variables

8x^2+10x-42=0

a = 8; b = 10; c = -42;
Δ = b2-4ac
Δ = 102-4·8·(-42)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-38}{2*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+38}{2*8}=\frac{28}{16}
=1+3/4
$