x(5x-8)=13-3x

Solution for x(5x-8)=13-3x equation:

x(5x-8)=13-3x

We move all terms to the left:

x(5x-8)-(13-3x)=0

We add all the numbers together, and all the variables

x(5x-8)-(-3x+13)=0

We multiply parentheses

5x^2-8x-(-3x+13)=0

We get rid of parentheses

5x^2-8x+3x-13=0

We add all the numbers together, and all the variables

5x^2-5x-13=0

a = 5; b = -5; c = -13;
Δ = b2-4ac
Δ = -52-4·5·(-13)
Δ = 285
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{285}}{2*5}=\frac{5-\sqrt{285}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{285}}{2*5}=\frac{5+\sqrt{285}}{10}
$