(X+5)(2x+3)4=16

Solution for (X+5)(2x+3)4=16 equation:

(X+5)(2X+3)4=16

We move all terms to the left:

(X+5)(2X+3)4-(16)=0

We multiply parentheses ..

(+2X^2+3X+10X+15)4-16=0

We multiply parentheses

8X^2+12X+40X+60-16=0

We add all the numbers together, and all the variables

8X^2+52X+44=0

a = 8; b = 52; c = +44;
Δ = b2-4ac
Δ = 522-4·8·44
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{-(52)-36}{2*8}=\frac{-88}{16}
=-5+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+36}{2*8}=\frac{-16}{16}
=-1
$