(2.5+x)(x)=37.5

Solution for (2.5+x)(x)=37.5 equation:

(2.5+x)(x)=37.5

We move all terms to the left:

(2.5+x)(x)-(37.5)=0

We add all the numbers together, and all the variables

(x+2.5)x-(37.5)=0

We add all the numbers together, and all the variables

(x+2.5)x-37.5=0

We multiply parentheses

x^2+2.5x-37.5=0

a = 1; b = 2.5; c = -37.5;
Δ = b2-4ac
Δ = 2.52-4·1·(-37.5)
Δ = 156.25
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{-(2.5)-\sqrt{156.25}}{2*1}=\frac{-2.5-\sqrt{156.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{156.25}}{2*1}=\frac{-2.5+\sqrt{156.25}}{2}
$