x^2+x=6/25

Solution for x^2+x=6/25 equation:

x^2+x=6/25

We move all terms to the left:

x^2+x-(6/25)=0

We add all the numbers together, and all the variables

x^2+x-(+6/25)=0

We get rid of parentheses

x^2+x-6/25=0

We multiply all the terms by the denominator


x^2*25+x*25-6=0

Wy multiply elements

25x^2+25x-6=0

a = 25; b = 25; c = -6;
Δ = b2-4ac
Δ = 252-4·25·(-6)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-35}{2*25}=\frac{-60}{50}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+35}{2*25}=\frac{10}{50}
=1/5
$