10x+140=x^2+2

Solution for 10x+140=x^2+2 equation:

10x+140=x^2+2

We move all terms to the left:

10x+140-(x^2+2)=0

We get rid of parentheses

-x^2+10x-2+140=0

We add all the numbers together, and all the variables

-1x^2+10x+138=0

a = -1; b = 10; c = +138;
Δ = b2-4ac
Δ = 102-4·(-1)·138
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{163}}{2*-1}=\frac{-10-2\sqrt{163}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{163}}{2*-1}=\frac{-10+2\sqrt{163}}{-2}
$