(X+1)(4x-8)=7

Solution for (X+1)(4x-8)=7 equation:

(X+1)(4X-8)=7

We move all terms to the left:

(X+1)(4X-8)-(7)=0

We multiply parentheses ..

(+4X^2-8X+4X-8)-7=0

We get rid of parentheses

4X^2-8X+4X-8-7=0

We add all the numbers together, and all the variables

4X^2-4X-15=0

a = 4; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·4·(-15)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*4}=\frac{-12}{8}
=-1+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*4}=\frac{20}{8}
=2+1/2
$