x+5x*x=38

Solution for x+5x*x=38 equation:

x+5x*x=38

We move all terms to the left:

x+5x*x-(38)=0

Wy multiply elements

5x^2+x-38=0

a = 5; b = 1; c = -38;
Δ = b2-4ac
Δ = 12-4·5·(-38)
Δ = 761
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{-(1)-\sqrt{761}}{2*5}=\frac{-1-\sqrt{761}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{761}}{2*5}=\frac{-1+\sqrt{761}}{10}
$