(2x+9)(2x+16)=198

Solution for (2x+9)(2x+16)=198 equation:

(2x+9)(2x+16)=198

We move all terms to the left:

(2x+9)(2x+16)-(198)=0

We multiply parentheses ..

(+4x^2+32x+18x+144)-198=0

We get rid of parentheses

4x^2+32x+18x+144-198=0

We add all the numbers together, and all the variables

4x^2+50x-54=0

a = 4; b = 50; c = -54;
Δ = b2-4ac
Δ = 502-4·4·(-54)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-58}{2*4}=\frac{-108}{8}
=-13+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+58}{2*4}=\frac{8}{8}
=1
$