48x^2+35x=83

Solution for 48x^2+35x=83 equation:

48x^2+35x=83

We move all terms to the left:

48x^2+35x-(83)=0

a = 48; b = 35; c = -83;
Δ = b2-4ac
Δ = 352-4·48·(-83)
Δ = 17161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17161}=131$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-131}{2*48}=\frac{-166}{96}
=-1+35/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+131}{2*48}=\frac{96}{96}
=1
$