X2+x/5=6/5

Solution for X2+x/5=6/5 equation:

X2+X/5=6/5

We move all terms to the left:

X2+X/5-(6/5)=0

We add all the numbers together, and all the variables

X2+X/5-(+6/5)=0

We add all the numbers together, and all the variables

X^2+X/5-(+6/5)=0

We get rid of parentheses

X^2+X/5-6/5=0

We multiply all the terms by the denominator


X^2*5+X-6=0

Wy multiply elements

5X^2+X-6=0

a = 5; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·5·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*5}=\frac{-12}{10}
=-1+1/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*5}=\frac{10}{10}
=1
$