5(x+1)-(-3x+1)=2(3x+5)10x=

Solution for 5(x+1)-(-3x+1)=2(3x+5)10x= equation:

5(x+1)-(-3x+1)=2(3x+5)10x=

We move all terms to the left:

5(x+1)-(-3x+1)-(2(3x+5)10x)=0

We multiply parentheses

5x-(-3x+1)-(2(3x+5)10x)+5=0

We get rid of parentheses

5x+3x-(2(3x+5)10x)-1+5=0


We calculate terms in parentheses: -(2(3x+5)10x), so:

2(3x+5)10x

We multiply parentheses

60x^2+100x

Back to the equation:

-(60x^2+100x)


We add all the numbers together, and all the variables

8x-(60x^2+100x)+4=0

We get rid of parentheses

-60x^2+8x-100x+4=0

We add all the numbers together, and all the variables

-60x^2-92x+4=0

a = -60; b = -92; c = +4;
Δ = b2-4ac
Δ = -922-4·(-60)·4
Δ = 9424
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:

$\sqrt{\Delta}=\sqrt{9424}=\sqrt{16*589}=\sqrt{16}*\sqrt{589}=4\sqrt{589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-4\sqrt{589}}{2*-60}=\frac{92-4\sqrt{589}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+4\sqrt{589}}{2*-60}=\frac{92+4\sqrt{589}}{-120}
$