4.61x2+43.4x+1620=7071

Solution for 4.61x2+43.4x+1620=7071 equation:

4.61x^2+43.4x+1620=7071

We move all terms to the left:

4.61x^2+43.4x+1620-(7071)=0

We add all the numbers together, and all the variables

4.61x^2+43.4x-5451=0

a = 4.61; b = 43.4; c = -5451;
Δ = b2-4ac
Δ = 43.42-4·4.61·(-5451)
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43.4)-320}{2*4.61}=\frac{-363.4}{9.22}
=-39+1/2.4136125654451
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43.4)+320}{2*4.61}=\frac{276.6}{9.22}
=30
$