3x^2-17x^2+10=0

Solution for 3x^2-17x^2+10=0 equation:

3x^2-17x^2+10=0

We add all the numbers together, and all the variables

-14x^2+10=0

a = -14; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-14)·10
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{35}}{2*-14}=\frac{0-4\sqrt{35}}{-28}
=-\frac{4\sqrt{35}}{-28}
=-\frac{\sqrt{35}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{35}}{2*-14}=\frac{0+4\sqrt{35}}{-28}
=\frac{4\sqrt{35}}{-28}
=\frac{\sqrt{35}}{-7}
$