5x^2-17x+19=2x^2

Solution for 5x^2-17x+19=2x^2 equation:

5x^2-17x+19=2x^2

We move all terms to the left:

5x^2-17x+19-(2x^2)=0

determiningTheFunctionDomain
5x^2-2x^2-17x+19=0

We add all the numbers together, and all the variables

3x^2-17x+19=0

a = 3; b = -17; c = +19;
Δ = b2-4ac
Δ = -172-4·3·19
Δ = 61
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{-(-17)-\sqrt{61}}{2*3}=\frac{17-\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{61}}{2*3}=\frac{17+\sqrt{61}}{6}
$