4x^2+((8.6*10^-4)x)-95.2=0

Solution for 4x^2+((8.6*10^-4)x)-95.2=0 equation:

4x^2+((8.6*10^-4)x)-95.2=0


We calculate terms in parentheses: +((8.6*10^-4)x), so:

(8.6*10^-4)x

We multiply parentheses

86x^2-4x

Back to the equation:

+(86x^2-4x)


We get rid of parentheses

4x^2+86x^2-4x-95.2=0

We add all the numbers together, and all the variables

90x^2-4x-95.2=0

a = 90; b = -4; c = -95.2;
Δ = b2-4ac
Δ = -42-4·90·(-95.2)
Δ = 34288
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:

$\sqrt{\Delta}=\sqrt{34288}=\sqrt{16*2143}=\sqrt{16}*\sqrt{2143}=4\sqrt{2143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2143}}{2*90}=\frac{4-4\sqrt{2143}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2143}}{2*90}=\frac{4+4\sqrt{2143}}{180}
$