1523x^2-1518x+253=0

Solution for 1523x^2-1518x+253=0 equation:

1523x^2-1518x+253=0

a = 1523; b = -1518; c = +253;
Δ = b2-4ac
Δ = -15182-4·1523·253
Δ = 763048
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:

$\sqrt{\Delta}=\sqrt{763048}=\sqrt{4*190762}=\sqrt{4}*\sqrt{190762}=2\sqrt{190762}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1518)-2\sqrt{190762}}{2*1523}=\frac{1518-2\sqrt{190762}}{3046}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1518)+2\sqrt{190762}}{2*1523}=\frac{1518+2\sqrt{190762}}{3046}
$