x(x+3.5)=65

Solution for x(x+3.5)=65 equation:

x(x+3.5)=65

We move all terms to the left:

x(x+3.5)-(65)=0

We multiply parentheses

x^2+3.5x-65=0

a = 1; b = 3.5; c = -65;
Δ = b2-4ac
Δ = 3.52-4·1·(-65)
Δ = 272.25
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{-(3.5)-\sqrt{272.25}}{2*1}=\frac{-3.5-\sqrt{272.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.5)+\sqrt{272.25}}{2*1}=\frac{-3.5+\sqrt{272.25}}{2}
$