1.25x(x+1)=0.5(2x-1)+3

Solution for 1.25x(x+1)=0.5(2x-1)+3 equation:

1.25x(x+1)=0.5(2x-1)+3

We move all terms to the left:

1.25x(x+1)-(0.5(2x-1)+3)=0

We multiply parentheses

x^2+x-(0.5(2x-1)+3)=0


We calculate terms in parentheses: -(0.5(2x-1)+3), so:

0.5(2x-1)+3

We multiply parentheses

x-0.5+3

We add all the numbers together, and all the variables

x+2.5

Back to the equation:

-(x+2.5)


We get rid of parentheses

x^2+x-x-2.5=0

We add all the numbers together, and all the variables

x^2-2.5=0

a = 1; b = 0; c = -2.5;
Δ = b2-4ac
Δ = 02-4·1·(-2.5)
Δ = 10
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{-(0)-\sqrt{10}}{2*1}=\frac{0-\sqrt{10}}{2}
=-\frac{\sqrt{}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{10}}{2*1}=\frac{0+\sqrt{10}}{2}
=\frac{\sqrt{}}{2}
$