5x^2-4x-43=0

Solution for 5x^2-4x-43=0 equation:

5x^2-4x-43=0

a = 5; b = -4; c = -43;
Δ = b2-4ac
Δ = -42-4·5·(-43)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{219}}{2*5}=\frac{4-2\sqrt{219}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{219}}{2*5}=\frac{4+2\sqrt{219}}{10}
$