(x^2-3x+6)+(-5x^2+7x+2)=0

Solution for (x^2-3x+6)+(-5x^2+7x+2)=0 equation:

(x^2-3x+6)+(-5x^2+7x+2)=0

We get rid of parentheses

-5x^2+x^2+7x-3x+2+6=0

We add all the numbers together, and all the variables

-4x^2+4x+8=0

a = -4; b = 4; c = +8;
Δ = b2-4ac
Δ = 42-4·(-4)·8
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{-(4)-12}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*-4}=\frac{8}{-8}
=-1
$