42=x2+4x-150

Solution for 42=x2+4x-150 equation:

42=x2+4x-150

We move all terms to the left:

42-(x2+4x-150)=0

We add all the numbers together, and all the variables

-(+x^2+4x-150)+42=0

We get rid of parentheses

-x^2-4x+150+42=0

We add all the numbers together, and all the variables

-1x^2-4x+192=0

a = -1; b = -4; c = +192;
Δ = b2-4ac
Δ = -42-4·(-1)·192
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-28}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+28}{2*-1}=\frac{32}{-2}
=-16
$