-3x^2+19x-43=-2x^2+11-27

Solution for -3x^2+19x-43=-2x^2+11-27 equation:

-3x^2+19x-43=-2x^2+11-27

We move all terms to the left:

-3x^2+19x-43-(-2x^2+11-27)=0

We get rid of parentheses

-3x^2+2x^2+19x-11+27-43=0

We add all the numbers together, and all the variables

-1x^2+19x-27=0

a = -1; b = 19; c = -27;
Δ = b2-4ac
Δ = 192-4·(-1)·(-27)
Δ = 253
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{253}}{2*-1}=\frac{-19-\sqrt{253}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{253}}{2*-1}=\frac{-19+\sqrt{253}}{-2}
$