3.5*10^(-8)=0.15x+x^2

Solution for 3.5*10^(-8)=0.15x+x^2 equation:

3.5*10^(-8)=0.15x+x^2

We move all terms to the left:

3.5*10^(-8)-(0.15x+x^2)=0

We add all the numbers together, and all the variables

-(0.15x+x^2)-8+3.5E=0

We get rid of parentheses

-x^2-0.15x-8+3.5E=0

We add all the numbers together, and all the variables

-1x^2-0.15x+1.5139863996067=0

a = -1; b = -0.15; c = +1.5139863996067;
Δ = b2-4ac
Δ = -0.152-4·(-1)·1.5139863996067
Δ = 6.0784455984268
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{-(-0.15)-\sqrt{6.0784455984268}}{2*-1}=\frac{0.15-\sqrt{6.0784455984268}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.15)+\sqrt{6.0784455984268}}{2*-1}=\frac{0.15+\sqrt{6.0784455984268}}{-2}
$