26x^2+10x=x+2

Solution for 26x^2+10x=x+2 equation:

26x^2+10x=x+2

We move all terms to the left:

26x^2+10x-(x+2)=0

We get rid of parentheses

26x^2+10x-x-2=0

We add all the numbers together, and all the variables

26x^2+9x-2=0

a = 26; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·26·(-2)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-17}{2*26}=\frac{-26}{52}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+17}{2*26}=\frac{8}{52}
=2/13
$