0,25(5+x)+0,75x(x+1)=5

Solution for 0,25(5+x)+0,75x(x+1)=5 equation:

0.25(5+x)+0.75x(x+1)=5

We move all terms to the left:

0.25(5+x)+0.75x(x+1)-(5)=0

We add all the numbers together, and all the variables

0.25(x+5)+0.75x(x+1)-5=0

We multiply parentheses

0x^2+0.25x+0x+1.25-5=0

We add all the numbers together, and all the variables

x^2+1.25x-3.75=0

a = 1; b = 1.25; c = -3.75;
Δ = b2-4ac
Δ = 1.252-4·1·(-3.75)
Δ = 16.5625
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{-(1.25)-\sqrt{16.5625}}{2*1}=\frac{-1.25-\sqrt{16.5625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.25)+\sqrt{16.5625}}{2*1}=\frac{-1.25+\sqrt{16.5625}}{2}
$