42x^2-480x-2461=0

Solution for 42x^2-480x-2461=0 equation:

42x^2-480x-2461=0

a = 42; b = -480; c = -2461;
Δ = b2-4ac
Δ = -4802-4·42·(-2461)
Δ = 643848
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:

$\sqrt{\Delta}=\sqrt{643848}=\sqrt{4*160962}=\sqrt{4}*\sqrt{160962}=2\sqrt{160962}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-2\sqrt{160962}}{2*42}=\frac{480-2\sqrt{160962}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+2\sqrt{160962}}{2*42}=\frac{480+2\sqrt{160962}}{84}
$