4x^2-12x-43=0

Solution for 4x^2-12x-43=0 equation:

4x^2-12x-43=0

a = 4; b = -12; c = -43;
Δ = b2-4ac
Δ = -122-4·4·(-43)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{13}}{2*4}=\frac{12-8\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{13}}{2*4}=\frac{12+8\sqrt{13}}{8}
$