3x^2-2x=4x^2-7

Solution for 3x^2-2x=4x^2-7 equation:

3x^2-2x=4x^2-7

We move all terms to the left:

3x^2-2x-(4x^2-7)=0

We get rid of parentheses

3x^2-4x^2-2x+7=0

We add all the numbers together, and all the variables

-1x^2-2x+7=0

a = -1; b = -2; c = +7;
Δ = b2-4ac
Δ = -22-4·(-1)·7
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{2}}{2*-1}=\frac{2-4\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{2}}{2*-1}=\frac{2+4\sqrt{2}}{-2}
$