4x(x+7)=32

Solution for 4x(x+7)=32 equation:

4x(x+7)=32

We move all terms to the left:

4x(x+7)-(32)=0

We multiply parentheses

4x^2+28x-32=0

a = 4; b = 28; c = -32;
Δ = b2-4ac
Δ = 282-4·4·(-32)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-36}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+36}{2*4}=\frac{8}{8}
=1
$