5x^2+8x=6x+3

Solution for 5x^2+8x=6x+3 equation:

5x^2+8x=6x+3

We move all terms to the left:

5x^2+8x-(6x+3)=0

We get rid of parentheses

5x^2+8x-6x-3=0

We add all the numbers together, and all the variables

5x^2+2x-3=0

a = 5; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·5·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8}{2*5}=\frac{6}{10}
=3/5
$