(2x)+(5x^2)=385

Solution for (2x)+(5x^2)=385 equation:

(2x)+(5x^2)=385

We move all terms to the left:

(2x)+(5x^2)-(385)=0

determiningTheFunctionDomain
5x^2+2x-385=0

a = 5; b = 2; c = -385;
Δ = b2-4ac
Δ = 22-4·5·(-385)
Δ = 7704
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:

$\sqrt{\Delta}=\sqrt{7704}=\sqrt{36*214}=\sqrt{36}*\sqrt{214}=6\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{214}}{2*5}=\frac{-2-6\sqrt{214}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{214}}{2*5}=\frac{-2+6\sqrt{214}}{10}
$