3.0=x^2-10x+21

Solution for 3.0=x^2-10x+21 equation:

3.0=x^2-10x+21

We move all terms to the left:

3.0-(x^2-10x+21)=0

We add all the numbers together, and all the variables

-(x^2-10x+21)+3=0

We get rid of parentheses

-x^2+10x-21+3=0

We add all the numbers together, and all the variables

-1x^2+10x-18=0

a = -1; b = 10; c = -18;
Δ = b2-4ac
Δ = 102-4·(-1)·(-18)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{7}}{2*-1}=\frac{-10-2\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{7}}{2*-1}=\frac{-10+2\sqrt{7}}{-2}
$