5.1x^2-1.5x-3.7=0

Solution for 5.1x^2-1.5x-3.7=0 equation:

5.1x^2-1.5x-3.7=0

a = 5.1; b = -1.5; c = -3.7;
Δ = b2-4ac
Δ = -1.52-4·5.1·(-3.7)
Δ = 77.73
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{-(-1.5)-\sqrt{77.73}}{2*5.1}=\frac{1.5-\sqrt{77.73}}{10.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{77.73}}{2*5.1}=\frac{1.5+\sqrt{77.73}}{10.2}
$