7x+5=(4x-8)4x+3x

Solution for 7x+5=(4x-8)4x+3x equation:

7x+5=(4x-8)4x+3x

We move all terms to the left:

7x+5-((4x-8)4x+3x)=0


We calculate terms in parentheses: -((4x-8)4x+3x), so:

(4x-8)4x+3x

We add all the numbers together, and all the variables

3x+(4x-8)4x

We multiply parentheses

16x^2+3x-32x

We add all the numbers together, and all the variables

16x^2-29x

Back to the equation:

-(16x^2-29x)


We get rid of parentheses

-16x^2+7x+29x+5=0

We add all the numbers together, and all the variables

-16x^2+36x+5=0

a = -16; b = 36; c = +5;
Δ = b2-4ac
Δ = 362-4·(-16)·5
Δ = 1616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{101}}{2*-16}=\frac{-36-4\sqrt{101}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{101}}{2*-16}=\frac{-36+4\sqrt{101}}{-32}
$