61.75=(2x+8)(2x+5)

Solution for 61.75=(2x+8)(2x+5) equation:

61.75=(2x+8)(2x+5)

We move all terms to the left:

61.75-((2x+8)(2x+5))=0

We multiply parentheses ..

-((+4x^2+10x+16x+40))+61.75=0


We calculate terms in parentheses: -((+4x^2+10x+16x+40)), so:

(+4x^2+10x+16x+40)

We get rid of parentheses

4x^2+10x+16x+40

We add all the numbers together, and all the variables

4x^2+26x+40

Back to the equation:

-(4x^2+26x+40)


We get rid of parentheses

-4x^2-26x-40+61.75=0

We add all the numbers together, and all the variables

-4x^2-26x+21.75=0

a = -4; b = -26; c = +21.75;
Δ = b2-4ac
Δ = -262-4·(-4)·21.75
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-32}{2*-4}=\frac{-6}{-8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+32}{2*-4}=\frac{58}{-8}
=-7+1/4
$