X^2-14x+21=-2x+7

Solution for X^2-14x+21=-2x+7 equation:

X^2-14X+21=-2X+7

We move all terms to the left:

X^2-14X+21-(-2X+7)=0

We get rid of parentheses

X^2-14X+2X-7+21=0

We add all the numbers together, and all the variables

X^2-12X+14=0

a = 1; b = -12; c = +14;
Δ = b2-4ac
Δ = -122-4·1·14
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{22}}{2*1}=\frac{12-2\sqrt{22}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{22}}{2*1}=\frac{12+2\sqrt{22}}{2}
$