4x+x*x=179

Solution for 4x+x*x=179 equation:

4x+x*x=179

We move all terms to the left:

4x+x*x-(179)=0

Wy multiply elements

x^2+4x-179=0

a = 1; b = 4; c = -179;
Δ = b2-4ac
Δ = 42-4·1·(-179)
Δ = 732
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{183}}{2*1}=\frac{-4-2\sqrt{183}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{183}}{2*1}=\frac{-4+2\sqrt{183}}{2}
$