40x^2=96x-39

Solution for 40x^2=96x-39 equation:

40x^2=96x-39

We move all terms to the left:

40x^2-(96x-39)=0

We get rid of parentheses

40x^2-96x+39=0

a = 40; b = -96; c = +39;
Δ = b2-4ac
Δ = -962-4·40·39
Δ = 2976
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:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{186}}{2*40}=\frac{96-4\sqrt{186}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{186}}{2*40}=\frac{96+4\sqrt{186}}{80}
$