-2x+7=2x^2-12x+19

Solution for -2x+7=2x^2-12x+19 equation:

-2x+7=2x^2-12x+19

We move all terms to the left:

-2x+7-(2x^2-12x+19)=0

We get rid of parentheses

-2x^2-2x+12x-19+7=0

We add all the numbers together, and all the variables

-2x^2+10x-12=0

a = -2; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·(-2)·(-12)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*-2}=\frac{-8}{-4}
=+2
$