5(8x2-x-4)=5(x+11)

Solution for 5(8x2-x-4)=5(x+11) equation:

5(8x^2-x-4)=5(x+11)

We move all terms to the left:

5(8x^2-x-4)-(5(x+11))=0

We multiply parentheses

40x^2-5x-(5(x+11))-20=0


We calculate terms in parentheses: -(5(x+11)), so:

5(x+11)

We multiply parentheses

5x+55

Back to the equation:

-(5x+55)


We get rid of parentheses

40x^2-5x-5x-55-20=0

We add all the numbers together, and all the variables

40x^2-10x-75=0

a = 40; b = -10; c = -75;
Δ = b2-4ac
Δ = -102-4·40·(-75)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-110}{2*40}=\frac{-100}{80}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+110}{2*40}=\frac{120}{80}
=1+1/2
$