5x^2=13x-8

Solution for 5x^2=13x-8 equation:

5x^2=13x-8

We move all terms to the left:

5x^2-(13x-8)=0

We get rid of parentheses

5x^2-13x+8=0

a = 5; b = -13; c = +8;
Δ = b2-4ac
Δ = -132-4·5·8
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3}{2*5}=\frac{16}{10}
=1+3/5
$