x^2-3x/5+8/5=10/5

Solution for x^2-3x/5+8/5=10/5 equation:

x^2-3x/5+8/5=10/5

We move all terms to the left:

x^2-3x/5+8/5-(10/5)=0

We add all the numbers together, and all the variables

x^2-3x/5+8/5-2=0

We add all the numbers together, and all the variables

x^2-3x/5-2+8/5=0

We multiply all the terms by the denominator


x^2*5-3x+8-2*5=0

We add all the numbers together, and all the variables

x^2*5-3x-2=0

Wy multiply elements

5x^2-3x-2=0

a = 5; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·5·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*5}=\frac{-4}{10}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*5}=\frac{10}{10}
=1
$