2x^2-126x+42=0

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

2x^2-126x+42=0

a = 2; b = -126; c = +42;
Δ = b2-4ac
Δ = -1262-4·2·42
Δ = 15540
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:

$\sqrt{\Delta}=\sqrt{15540}=\sqrt{4*3885}=\sqrt{4}*\sqrt{3885}=2\sqrt{3885}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3885}}{2*2}=\frac{126-2\sqrt{3885}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3885}}{2*2}=\frac{126+2\sqrt{3885}}{4}
$