-48x^2+176x-141=0

Solution for -48x^2+176x-141=0 equation:

-48x^2+176x-141=0

a = -48; b = 176; c = -141;
Δ = b2-4ac
Δ = 1762-4·(-48)·(-141)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-8\sqrt{61}}{2*-48}=\frac{-176-8\sqrt{61}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+8\sqrt{61}}{2*-48}=\frac{-176+8\sqrt{61}}{-96}
$