7-4x2=3x2-2x+5

Solution for 7-4x2=3x2-2x+5 equation:

7-4x^2=3x^2-2x+5

We move all terms to the left:

7-4x^2-(3x^2-2x+5)=0

We get rid of parentheses

-4x^2-3x^2+2x-5+7=0

We add all the numbers together, and all the variables

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

a = -7; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-7)·2
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{15}}{2*-7}=\frac{-2-2\sqrt{15}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{15}}{2*-7}=\frac{-2+2\sqrt{15}}{-14}
$