42+x2-5x=6+180

Solution for 42+x2-5x=6+180 equation:

42+x2-5x=6+180

We move all terms to the left:

42+x2-5x-(6+180)=0

We add all the numbers together, and all the variables

x2-5x+42-186=0

We add all the numbers together, and all the variables

x^2-5x-144=0

a = 1; b = -5; c = -144;
Δ = b2-4ac
Δ = -52-4·1·(-144)
Δ = 601
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{-(-5)-\sqrt{601}}{2*1}=\frac{5-\sqrt{601}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{601}}{2*1}=\frac{5+\sqrt{601}}{2}
$