10x+140=10x^2+2

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

10x+140=10x^2+2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -10; b = 10; c = +138;
Δ = b2-4ac
Δ = 102-4·(-10)·138
Δ = 5620
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:

$\sqrt{\Delta}=\sqrt{5620}=\sqrt{4*1405}=\sqrt{4}*\sqrt{1405}=2\sqrt{1405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{1405}}{2*-10}=\frac{-10-2\sqrt{1405}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{1405}}{2*-10}=\frac{-10+2\sqrt{1405}}{-20}
$