(2w+10)(2w+9)=120.75

Solution for (2w+10)(2w+9)=120.75 equation:

(2w+10)(2w+9)=120.75

We move all terms to the left:

(2w+10)(2w+9)-(120.75)=0

We add all the numbers together, and all the variables

(2w+10)(2w+9)-120.75=0

We multiply parentheses ..

(+4w^2+18w+20w+90)-120.75=0

We get rid of parentheses

4w^2+18w+20w+90-120.75=0

We add all the numbers together, and all the variables

4w^2+38w-30.75=0

a = 4; b = 38; c = -30.75;
Δ = b2-4ac
Δ = 382-4·4·(-30.75)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-44}{2*4}=\frac{-82}{8}
=-10+1/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+44}{2*4}=\frac{6}{8}
=3/4
$