8x^2=5(x+2)

Solution for 8x^2=5(x+2) equation:

8x^2=5(x+2)

We move all terms to the left:

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


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

5(x+2)

We multiply parentheses

5x+10

Back to the equation:

-(5x+10)


We get rid of parentheses

8x^2-5x-10=0

a = 8; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·8·(-10)
Δ = 345
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{345}}{2*8}=\frac{5-\sqrt{345}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{345}}{2*8}=\frac{5+\sqrt{345}}{16}
$