4.20x^2-2.71x-1.42=0

Solution for 4.20x^2-2.71x-1.42=0 equation:

4.20x^2-2.71x-1.42=0

a = 4.20; b = -2.71; c = -1.42;
Δ = b2-4ac
Δ = -2.712-4·4.20·(-1.42)
Δ = 31.2001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.71)-\sqrt{31.2001}}{2*4.20}=\frac{2.71-\sqrt{31.2001}}{8.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.71)+\sqrt{31.2001}}{2*4.20}=\frac{2.71+\sqrt{31.2001}}{8.4}
$