X2-5x-(1513/48)=0

Solution for X2-5x-(1513/48)=0 equation:

X2-5X-(1513/48)=0

We add all the numbers together, and all the variables

X2-5X-(+1513/48)=0

We add all the numbers together, and all the variables

X^2-5X-(+1513/48)=0

We get rid of parentheses

X^2-5X-1513/48=0

We multiply all the terms by the denominator


X^2*48-5X*48-1513=0

Wy multiply elements

48X^2-240X-1513=0

a = 48; b = -240; c = -1513;
Δ = b2-4ac
Δ = -2402-4·48·(-1513)
Δ = 348096
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:

$\sqrt{\Delta}=\sqrt{348096}=\sqrt{3136*111}=\sqrt{3136}*\sqrt{111}=56\sqrt{111}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-56\sqrt{111}}{2*48}=\frac{240-56\sqrt{111}}{96}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+56\sqrt{111}}{2*48}=\frac{240+56\sqrt{111}}{96}
$