42x^2-126x-100=0

Solution for 42x^2-126x-100=0 equation:

42x^2-126x-100=0

a = 42; b = -126; c = -100;
Δ = b2-4ac
Δ = -1262-4·42·(-100)
Δ = 32676
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:

$\sqrt{\Delta}=\sqrt{32676}=\sqrt{4*8169}=\sqrt{4}*\sqrt{8169}=2\sqrt{8169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{8169}}{2*42}=\frac{126-2\sqrt{8169}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{8169}}{2*42}=\frac{126+2\sqrt{8169}}{84}
$