5x2+6x-12=0

Solution for 5x2+6x-12=0 equation:

5x^2+6x-12=0

a = 5; b = 6; c = -12;
Δ = b2-4ac
Δ = 62-4·5·(-12)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*5}=\frac{-6-2\sqrt{69}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*5}=\frac{-6+2\sqrt{69}}{10}
$