4x^2+42x-54=0

Solution for 4x^2+42x-54=0 equation:

4x^2+42x-54=0

a = 4; b = 42; c = -54;
Δ = b2-4ac
Δ = 422-4·4·(-54)
Δ = 2628
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:

$\sqrt{\Delta}=\sqrt{2628}=\sqrt{36*73}=\sqrt{36}*\sqrt{73}=6\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{73}}{2*4}=\frac{-42-6\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{73}}{2*4}=\frac{-42+6\sqrt{73}}{8}
$