2x^2+8=42-x

Solution for 2x^2+8=42-x equation:

2x^2+8=42-x

We move all terms to the left:

2x^2+8-(42-x)=0

We add all the numbers together, and all the variables

2x^2-(-1x+42)+8=0

We get rid of parentheses

2x^2+1x-42+8=0

We add all the numbers together, and all the variables

2x^2+x-34=0

a = 2; b = 1; c = -34;
Δ = b2-4ac
Δ = 12-4·2·(-34)
Δ = 273
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{273}}{2*2}=\frac{-1-\sqrt{273}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{273}}{2*2}=\frac{-1+\sqrt{273}}{4}
$