25x^2-45x-21=0

Solution for 25x^2-45x-21=0 equation:

25x^2-45x-21=0

a = 25; b = -45; c = -21;
Δ = b2-4ac
Δ = -452-4·25·(-21)
Δ = 4125
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:

$\sqrt{\Delta}=\sqrt{4125}=\sqrt{25*165}=\sqrt{25}*\sqrt{165}=5\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5\sqrt{165}}{2*25}=\frac{45-5\sqrt{165}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5\sqrt{165}}{2*25}=\frac{45+5\sqrt{165}}{50}
$