0=7x^2-31x+26

Solution for 0=7x^2-31x+26 equation:

0=7x^2-31x+26

We move all terms to the left:

0-(7x^2-31x+26)=0

We add all the numbers together, and all the variables

-(7x^2-31x+26)=0

We get rid of parentheses

-7x^2+31x-26=0

a = -7; b = 31; c = -26;
Δ = b2-4ac
Δ = 312-4·(-7)·(-26)
Δ = 233
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{-(31)-\sqrt{233}}{2*-7}=\frac{-31-\sqrt{233}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{233}}{2*-7}=\frac{-31+\sqrt{233}}{-14}
$