4x^2+16x=6(4x+10)

Solution for 4x^2+16x=6(4x+10) equation:

4x^2+16x=6(4x+10)

We move all terms to the left:

4x^2+16x-(6(4x+10))=0


We calculate terms in parentheses: -(6(4x+10)), so:

6(4x+10)

We multiply parentheses

24x+60

Back to the equation:

-(24x+60)


We get rid of parentheses

4x^2+16x-24x-60=0

We add all the numbers together, and all the variables

4x^2-8x-60=0

a = 4; b = -8; c = -60;
Δ = b2-4ac
Δ = -82-4·4·(-60)
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{-(-8)-32}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+32}{2*4}=\frac{40}{8}
=5
$