(2x)^2+(x-1)=13^2

Solution for (2x)^2+(x-1)=13^2 equation:

(2x)^2+(x-1)=13^2

We move all terms to the left:

(2x)^2+(x-1)-(13^2)=0

We add all the numbers together, and all the variables

2x^2+(x-1)-169=0

We get rid of parentheses

2x^2+x-1-169=0

We add all the numbers together, and all the variables

2x^2+x-170=0

a = 2; b = 1; c = -170;
Δ = b2-4ac
Δ = 12-4·2·(-170)
Δ = 1361
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)-\sqrt{1361}}{2*2}=\frac{-1-\sqrt{1361}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1361}}{2*2}=\frac{-1+\sqrt{1361}}{4}
$