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

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

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

We move all terms to the left:

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

We multiply parentheses

24x^2-56x-((4x-5)+3x)=0


We calculate terms in parentheses: -((4x-5)+3x), so:

(4x-5)+3x

We add all the numbers together, and all the variables

3x+(4x-5)

We get rid of parentheses

3x+4x-5

We add all the numbers together, and all the variables

7x-5

Back to the equation:

-(7x-5)


We get rid of parentheses

24x^2-56x-7x+5=0

We add all the numbers together, and all the variables

24x^2-63x+5=0

a = 24; b = -63; c = +5;
Δ = b2-4ac
Δ = -632-4·24·5
Δ = 3489
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{-(-63)-\sqrt{3489}}{2*24}=\frac{63-\sqrt{3489}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{3489}}{2*24}=\frac{63+\sqrt{3489}}{48}
$