25x^2+30x-23=0

Solution for 25x^2+30x-23=0 equation:

25x^2+30x-23=0

a = 25; b = 30; c = -23;
Δ = b2-4ac
Δ = 302-4·25·(-23)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-40\sqrt{2}}{2*25}=\frac{-30-40\sqrt{2}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+40\sqrt{2}}{2*25}=\frac{-30+40\sqrt{2}}{50}
$