x^2-(8/5)x+(7/10)=0

Solution for x^2-(8/5)x+(7/10)=0 equation:

x^2-(8/5)x+(7/10)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x^2-(+8/5)x+(+7/10)=0

We multiply parentheses

x^2-8x^2+(+7/10)=0

We get rid of parentheses

x^2-8x^2+7/10=0

We multiply all the terms by the denominator


x^2*10-8x^2*10+7=0

Wy multiply elements

10x^2-80x^2+7=0

We add all the numbers together, and all the variables

-70x^2+7=0

a = -70; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-70)·7
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{10}}{2*-70}=\frac{0-14\sqrt{10}}{-140}
=-\frac{14\sqrt{10}}{-140}
=-\frac{\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{10}}{2*-70}=\frac{0+14\sqrt{10}}{-140}
=\frac{14\sqrt{10}}{-140}
=\frac{\sqrt{10}}{-10}
$