7x^2-4x-17=5x^2

Solution for 7x^2-4x-17=5x^2 equation:

7x^2-4x-17=5x^2

We move all terms to the left:

7x^2-4x-17-(5x^2)=0

determiningTheFunctionDomain
7x^2-5x^2-4x-17=0

We add all the numbers together, and all the variables

2x^2-4x-17=0

a = 2; b = -4; c = -17;
Δ = b2-4ac
Δ = -42-4·2·(-17)
Δ = 152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{38}}{2*2}=\frac{4-2\sqrt{38}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{38}}{2*2}=\frac{4+2\sqrt{38}}{4}
$