2x^2-13x+7=x^2

Solution for 2x^2-13x+7=x^2 equation:

2x^2-13x+7=x^2

We move all terms to the left:

2x^2-13x+7-(x^2)=0

determiningTheFunctionDomain
2x^2-x^2-13x+7=0

We add all the numbers together, and all the variables

x^2-13x+7=0

a = 1; b = -13; c = +7;
Δ = b2-4ac
Δ = -132-4·1·7
Δ = 141
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{-(-13)-\sqrt{141}}{2*1}=\frac{13-\sqrt{141}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{141}}{2*1}=\frac{13+\sqrt{141}}{2}
$