5-x=2x^2-71

Solution for 5-x=2x^2-71 equation:

5-x=2x^2-71

We move all terms to the left:

5-x-(2x^2-71)=0

We add all the numbers together, and all the variables

-1x-(2x^2-71)+5=0

We get rid of parentheses

-2x^2-1x+71+5=0

We add all the numbers together, and all the variables

-2x^2-1x+76=0

a = -2; b = -1; c = +76;
Δ = b2-4ac
Δ = -12-4·(-2)·76
Δ = 609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{609}}{2*-2}=\frac{1-\sqrt{609}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{609}}{2*-2}=\frac{1+\sqrt{609}}{-4}
$