65+65x=2.3x^2

Solution for 65+65x=2.3x^2 equation:

65+65x=2.3x^2

We move all terms to the left:

65+65x-(2.3x^2)=0

We get rid of parentheses

-2.3x^2+65x+65=0

a = -2.3; b = 65; c = +65;
Δ = b2-4ac
Δ = 652-4·(-2.3)·65
Δ = 4823
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{-(65)-\sqrt{4823}}{2*-2.3}=\frac{-65-\sqrt{4823}}{-4.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4823}}{2*-2.3}=\frac{-65+\sqrt{4823}}{-4.6}
$