3x-5=-8(6+5x)x=

Solution for 3x-5=-8(6+5x)x= equation:

3x-5=-8(6+5x)x=

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(-8(5x+6)x), so:

-8(5x+6)x

We multiply parentheses

-40x^2-48x

Back to the equation:

-(-40x^2-48x)


We get rid of parentheses

40x^2+48x+3x-5=0

We add all the numbers together, and all the variables

40x^2+51x-5=0

a = 40; b = 51; c = -5;
Δ = b2-4ac
Δ = 512-4·40·(-5)
Δ = 3401
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{-(51)-\sqrt{3401}}{2*40}=\frac{-51-\sqrt{3401}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{3401}}{2*40}=\frac{-51+\sqrt{3401}}{80}
$