(3x+7)(3x+7)=2.5

Solution for (3x+7)(3x+7)=2.5 equation:

(3x+7)(3x+7)=2.5

We move all terms to the left:

(3x+7)(3x+7)-(2.5)=0

We add all the numbers together, and all the variables

(3x+7)(3x+7)-2.5=0

We multiply parentheses ..

(+9x^2+21x+21x+49)-2.5=0

We get rid of parentheses

9x^2+21x+21x+49-2.5=0

We add all the numbers together, and all the variables

9x^2+42x+46.5=0

a = 9; b = 42; c = +46.5;
Δ = b2-4ac
Δ = 422-4·9·46.5
Δ = 90
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{90}=\sqrt{9*10}=\sqrt{9}*\sqrt{10}=3\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-3\sqrt{10}}{2*9}=\frac{-42-3\sqrt{10}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+3\sqrt{10}}{2*9}=\frac{-42+3\sqrt{10}}{18}
$