x2+2=10x+140

Solution for x2+2=10x+140 equation:

x2+2=10x+140

We move all terms to the left:

x2+2-(10x+140)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^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}
$