5x^2+12x-57=0

Solution for 5x^2+12x-57=0 equation:

5x^2+12x-57=0

a = 5; b = 12; c = -57;
Δ = b2-4ac
Δ = 122-4·5·(-57)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{321}}{2*5}=\frac{-12-2\sqrt{321}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{321}}{2*5}=\frac{-12+2\sqrt{321}}{10}
$