-x^2+4x-6=4x^2-14x+3

Solution for -x^2+4x-6=4x^2-14x+3 equation:

-x^2+4x-6=4x^2-14x+3

We move all terms to the left:

-x^2+4x-6-(4x^2-14x+3)=0

We add all the numbers together, and all the variables

-1x^2+4x-(4x^2-14x+3)-6=0

We get rid of parentheses

-1x^2-4x^2+4x+14x-3-6=0

We add all the numbers together, and all the variables

-5x^2+18x-9=0

a = -5; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·(-5)·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12}{2*-5}=\frac{-30}{-10}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12}{2*-5}=\frac{-6}{-10}
=3/5
$