4x(2x+4)=10x+15-2x+1

Solution for 4x(2x+4)=10x+15-2x+1 equation:

4x(2x+4)=10x+15-2x+1

We move all terms to the left:

4x(2x+4)-(10x+15-2x+1)=0

We add all the numbers together, and all the variables

4x(2x+4)-(8x+16)=0

We multiply parentheses

8x^2+16x-(8x+16)=0

We get rid of parentheses

8x^2+16x-8x-16=0

We add all the numbers together, and all the variables

8x^2+8x-16=0

a = 8; b = 8; c = -16;
Δ = b2-4ac
Δ = 82-4·8·(-16)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-24}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+24}{2*8}=\frac{16}{16}
=1
$