5x^2=8x+3

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

5x^2=8x+3

We move all terms to the left:

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

We get rid of parentheses

5x^2-8x-3=0

a = 5; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·5·(-3)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{31}}{2*5}=\frac{8-2\sqrt{31}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{31}}{2*5}=\frac{8+2\sqrt{31}}{10}
$