x^2-10x-(21/10)=0

Solution for x^2-10x-(21/10)=0 equation:

x^2-10x-(21/10)=0

We add all the numbers together, and all the variables

x^2-10x-(+21/10)=0

We get rid of parentheses

x^2-10x-21/10=0

We multiply all the terms by the denominator


x^2*10-10x*10-21=0

Wy multiply elements

10x^2-100x-21=0

a = 10; b = -100; c = -21;
Δ = b2-4ac
Δ = -1002-4·10·(-21)
Δ = 10840
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:

$\sqrt{\Delta}=\sqrt{10840}=\sqrt{4*2710}=\sqrt{4}*\sqrt{2710}=2\sqrt{2710}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2710}}{2*10}=\frac{100-2\sqrt{2710}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2710}}{2*10}=\frac{100+2\sqrt{2710}}{20}
$