3x2-7x2+2=05x2+13x2-46=0

Solution for 3x2-7x2+2=05x2+13x2-46=0 equation:

3x^2-7x^2+2=05x^2+13x^2-46=0

We move all terms to the left:

3x^2-7x^2+2-(05x^2+13x^2-46)=0

We add all the numbers together, and all the variables

-4x^2-(05x^2+13x^2-46)+2=0

We get rid of parentheses

-4x^2-05x^2-13x^2+46+2=0

We add all the numbers together, and all the variables

-22x^2+48=0

a = -22; b = 0; c = +48;
Δ = b2-4ac
Δ = 02-4·(-22)·48
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{66}}{2*-22}=\frac{0-8\sqrt{66}}{-44}
=-\frac{8\sqrt{66}}{-44}
=-\frac{2\sqrt{66}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{66}}{2*-22}=\frac{0+8\sqrt{66}}{-44}
=\frac{8\sqrt{66}}{-44}
=\frac{2\sqrt{66}}{-11}
$