8x-3=5(2x+1)8x-3=5(2x+1)

Solution for 8x-3=5(2x+1)8x-3=5(2x+1) equation:

8x-3=5(2x+1)8x-3=5(2x+1)

We move all terms to the left:

8x-3-(5(2x+1)8x-3)=0


We calculate terms in parentheses: -(5(2x+1)8x-3), so:

5(2x+1)8x-3

We multiply parentheses

80x^2+40x-3

Back to the equation:

-(80x^2+40x-3)


We get rid of parentheses

-80x^2+8x-40x+3-3=0

We add all the numbers together, and all the variables

-80x^2-32x=0

a = -80; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-80)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-80}=\frac{0}{-160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-80}=\frac{64}{-160}
=-2/5
$