x2-7x+4=46

Solution for x2-7x+4=46 equation:

x2-7x+4=46

We move all terms to the left:

x2-7x+4-(46)=0

We add all the numbers together, and all the variables

x^2-7x-42=0

a = 1; b = -7; c = -42;
Δ = b2-4ac
Δ = -72-4·1·(-42)
Δ = 217
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{-(-7)-\sqrt{217}}{2*1}=\frac{7-\sqrt{217}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{217}}{2*1}=\frac{7+\sqrt{217}}{2}
$