0.05x+x^2=0.975

Solution for 0.05x+x^2=0.975 equation:

0.05x+x^2=0.975

We move all terms to the left:

0.05x+x^2-(0.975)=0

We add all the numbers together, and all the variables

x^2+0.05x-0.975=0

a = 1; b = 0.05; c = -0.975;
Δ = b2-4ac
Δ = 0.052-4·1·(-0.975)
Δ = 3.9025
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{-(0.05)-\sqrt{3.9025}}{2*1}=\frac{-0.05-\sqrt{3.9025}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.05)+\sqrt{3.9025}}{2*1}=\frac{-0.05+\sqrt{3.9025}}{2}
$