25x^2-75x+46=0

Solution for 25x^2-75x+46=0 equation:

25x^2-75x+46=0

a = 25; b = -75; c = +46;
Δ = b2-4ac
Δ = -752-4·25·46
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{41}}{2*25}=\frac{75-5\sqrt{41}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{41}}{2*25}=\frac{75+5\sqrt{41}}{50}
$