x(x+2.5)=21

Solution for x(x+2.5)=21 equation:

x(x+2.5)=21

We move all terms to the left:

x(x+2.5)-(21)=0

We multiply parentheses

x^2+2.5x-21=0

a = 1; b = 2.5; c = -21;
Δ = b2-4ac
Δ = 2.52-4·1·(-21)
Δ = 90.25
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{90.25}}{2*1}=\frac{-2.5-\sqrt{90.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{90.25}}{2*1}=\frac{-2.5+\sqrt{90.25}}{2}
$