6x-7=21-x2

Solution for 6x-7=21-x2 equation:

6x-7=21-x2

We move all terms to the left:

6x-7-(21-x2)=0

We add all the numbers together, and all the variables

-(-1x^2+21)+6x-7=0

We get rid of parentheses

1x^2+6x-21-7=0

We add all the numbers together, and all the variables

x^2+6x-28=0

a = 1; b = 6; c = -28;
Δ = b2-4ac
Δ = 62-4·1·(-28)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{37}}{2*1}=\frac{-6-2\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{37}}{2*1}=\frac{-6+2\sqrt{37}}{2}
$