17=3x^2+4x^2

Solution for 17=3x^2+4x^2 equation:

17=3x^2+4x^2

We move all terms to the left:

17-(3x^2+4x^2)=0

We get rid of parentheses

-3x^2-4x^2+17=0

We add all the numbers together, and all the variables

-7x^2+17=0

a = -7; b = 0; c = +17;
Δ = b2-4ac
Δ = 02-4·(-7)·17
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{119}}{2*-7}=\frac{0-2\sqrt{119}}{-14}
=-\frac{2\sqrt{119}}{-14}
=-\frac{\sqrt{119}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{119}}{2*-7}=\frac{0+2\sqrt{119}}{-14}
=\frac{2\sqrt{119}}{-14}
=\frac{\sqrt{119}}{-7}
$