(4x+5)+(x*x+10)=180

Solution for (4x+5)+(x*x+10)=180 equation:

(4x+5)+(x*x+10)=180

We move all terms to the left:

(4x+5)+(x*x+10)-(180)=0

We get rid of parentheses

4x+x*x+5+10-180=0

We add all the numbers together, and all the variables

4x+x*x-165=0

Wy multiply elements

x^2+4x-165=0

a = 1; b = 4; c = -165;
Δ = b2-4ac
Δ = 42-4·1·(-165)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-26}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+26}{2*1}=\frac{22}{2}
=11
$