(2x+3.25)(2x+3)=15

Solution for (2x+3.25)(2x+3)=15 equation:

(2x+3.25)(2x+3)=15

We move all terms to the left:

(2x+3.25)(2x+3)-(15)=0

We multiply parentheses ..

(+4x^2+6x+6.5x+9.75)-15=0

We get rid of parentheses

4x^2+6x+6.5x+9.75-15=0

We add all the numbers together, and all the variables

4x^2+12.5x-5.25=0

a = 4; b = 12.5; c = -5.25;
Δ = b2-4ac
Δ = 12.52-4·4·(-5.25)
Δ = 240.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12.5)-\sqrt{240.25}}{2*4}=\frac{-12.5-\sqrt{240.25}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12.5)+\sqrt{240.25}}{2*4}=\frac{-12.5+\sqrt{240.25}}{8}
$