-12x+7=5-2x2

Solution for -12x+7=5-2x2 equation:

-12x+7=5-2x^2

We move all terms to the left:

-12x+7-(5-2x^2)=0

We get rid of parentheses

2x^2-12x-5+7=0

We add all the numbers together, and all the variables

2x^2-12x+2=0

a = 2; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·2·2
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{2}}{2*2}=\frac{12-8\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{2}}{2*2}=\frac{12+8\sqrt{2}}{4}
$