4x(4x-8)=(5x-15)

Solution for 4x(4x-8)=(5x-15) equation:

4x(4x-8)=(5x-15)

We move all terms to the left:

4x(4x-8)-((5x-15))=0

We multiply parentheses

16x^2-32x-((5x-15))=0


We calculate terms in parentheses: -((5x-15)), so:

(5x-15)

We get rid of parentheses

5x-15

Back to the equation:

-(5x-15)


We get rid of parentheses

16x^2-32x-5x+15=0

We add all the numbers together, and all the variables

16x^2-37x+15=0

a = 16; b = -37; c = +15;
Δ = b2-4ac
Δ = -372-4·16·15
Δ = 409
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{-(-37)-\sqrt{409}}{2*16}=\frac{37-\sqrt{409}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{409}}{2*16}=\frac{37+\sqrt{409}}{32}
$