(4x+10)+(6x^2)=180

Solution for (4x+10)+(6x^2)=180 equation:

(4x+10)+(6x^2)=180

We move all terms to the left:

(4x+10)+(6x^2)-(180)=0

determiningTheFunctionDomain
6x^2+(4x+10)-180=0

We get rid of parentheses

6x^2+4x+10-180=0

We add all the numbers together, and all the variables

6x^2+4x-170=0

a = 6; b = 4; c = -170;
Δ = b2-4ac
Δ = 42-4·6·(-170)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-64}{2*6}=\frac{-68}{12}
=-5+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+64}{2*6}=\frac{60}{12}
=5
$