3x-(2x-1)=7x(3-5x)+(3-5x)+(-x+24)

Solution for 3x-(2x-1)=7x(3-5x)+(3-5x)+(-x+24) equation:

3x-(2x-1)=7x(3-5x)+(3-5x)+(-x+24)

We move all terms to the left:

3x-(2x-1)-(7x(3-5x)+(3-5x)+(-x+24))=0

We add all the numbers together, and all the variables

3x-(2x-1)-(7x(-5x+3)+(-5x+3)+(-1x+24))=0

We get rid of parentheses

3x-2x-(7x(-5x+3)+(-5x+3)+(-1x+24))+1=0


We calculate terms in parentheses: -(7x(-5x+3)+(-5x+3)+(-1x+24)), so:

7x(-5x+3)+(-5x+3)+(-1x+24)

We multiply parentheses

-35x^2+21x+(-5x+3)+(-1x+24)

We get rid of parentheses

-35x^2+21x-5x-1x+3+24

We add all the numbers together, and all the variables

-35x^2+15x+27

Back to the equation:

-(-35x^2+15x+27)


We add all the numbers together, and all the variables

-(-35x^2+15x+27)+x+1=0

We get rid of parentheses

35x^2-15x+x-27+1=0

We add all the numbers together, and all the variables

35x^2-14x-26=0

a = 35; b = -14; c = -26;
Δ = b2-4ac
Δ = -142-4·35·(-26)
Δ = 3836
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:

$\sqrt{\Delta}=\sqrt{3836}=\sqrt{4*959}=\sqrt{4}*\sqrt{959}=2\sqrt{959}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{959}}{2*35}=\frac{14-2\sqrt{959}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{959}}{2*35}=\frac{14+2\sqrt{959}}{70}
$