-x^2=-142+2x

Solution for -x^2=-142+2x equation:

-x^2=-142+2x

We move all terms to the left:

-x^2-(-142+2x)=0

We add all the numbers together, and all the variables

-x^2-(2x-142)=0

We add all the numbers together, and all the variables

-1x^2-(2x-142)=0

We get rid of parentheses

-1x^2-2x+142=0

a = -1; b = -2; c = +142;
Δ = b2-4ac
Δ = -22-4·(-1)·142
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{143}}{2*-1}=\frac{2-2\sqrt{143}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{143}}{2*-1}=\frac{2+2\sqrt{143}}{-2}
$