2x(x+1.25)=3.5

Solution for 2x(x+1.25)=3.5 equation:

2x(x+1.25)=3.5

We move all terms to the left:

2x(x+1.25)-(3.5)=0

We add all the numbers together, and all the variables

2x(x+1.25)-3.5=0

We multiply parentheses

2x^2+2.5x-3.5=0

a = 2; b = 2.5; c = -3.5;
Δ = b2-4ac
Δ = 2.52-4·2·(-3.5)
Δ = 34.25
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{34.25}}{2*2}=\frac{-2.5-\sqrt{34.25}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{34.25}}{2*2}=\frac{-2.5+\sqrt{34.25}}{4}
$