12.5x^2+30x-52=0

Solution for 12.5x^2+30x-52=0 equation:

12.5x^2+30x-52=0

a = 12.5; b = 30; c = -52;
Δ = b2-4ac
Δ = 302-4·12.5·(-52)
Δ = 3500
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:

$\sqrt{\Delta}=\sqrt{3500}=\sqrt{100*35}=\sqrt{100}*\sqrt{35}=10\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{35}}{2*12.5}=\frac{-30-10\sqrt{35}}{25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{35}}{2*12.5}=\frac{-30+10\sqrt{35}}{25}
$