25x^2-42-65x=0

Solution for 25x^2-42-65x=0 equation:

25x^2-42-65x=0

a = 25; b = -65; c = -42;
Δ = b2-4ac
Δ = -652-4·25·(-42)
Δ = 8425
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:

$\sqrt{\Delta}=\sqrt{8425}=\sqrt{25*337}=\sqrt{25}*\sqrt{337}=5\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-5\sqrt{337}}{2*25}=\frac{65-5\sqrt{337}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+5\sqrt{337}}{2*25}=\frac{65+5\sqrt{337}}{50}
$