95x^2+44x+1=33

Solution for 95x^2+44x+1=33 equation:

95x^2+44x+1=33

We move all terms to the left:

95x^2+44x+1-(33)=0

We add all the numbers together, and all the variables

95x^2+44x-32=0

a = 95; b = 44; c = -32;
Δ = b2-4ac
Δ = 442-4·95·(-32)
Δ = 14096
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:

$\sqrt{\Delta}=\sqrt{14096}=\sqrt{16*881}=\sqrt{16}*\sqrt{881}=4\sqrt{881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{881}}{2*95}=\frac{-44-4\sqrt{881}}{190}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{881}}{2*95}=\frac{-44+4\sqrt{881}}{190}
$