X^2-6x+4=-3

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

X^2-6X+4=-3

We move all terms to the left:

X^2-6X+4-(-3)=0

We add all the numbers together, and all the variables

X^2-6X+7=0

a = 1; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·1·7
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{2}}{2*1}=\frac{6-2\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{2}}{2*1}=\frac{6+2\sqrt{2}}{2}
$