5x*x-3x=8

Solution for 5x*x-3x=8 equation:

5x*x-3x=8

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

Wy multiply elements

5x^2-3x-8=0

a = 5; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·5·(-8)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*5}=\frac{16}{10}
=1+3/5
$