-5x^2+12x+3=0

Solution for -5x^2+12x+3=0 equation:

-5x^2+12x+3=0

a = -5; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·(-5)·3
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{51}}{2*-5}=\frac{-12-2\sqrt{51}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{51}}{2*-5}=\frac{-12+2\sqrt{51}}{-10}
$