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

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

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

We move all terms to the left:

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

We multiply parentheses

3x-10x-(5x(2x+7))-2=0


We calculate terms in parentheses: -(5x(2x+7)), so:

5x(2x+7)

We multiply parentheses

10x^2+35x

Back to the equation:

-(10x^2+35x)


We add all the numbers together, and all the variables

-7x-(10x^2+35x)-2=0

We get rid of parentheses

-10x^2-7x-35x-2=0

We add all the numbers together, and all the variables

-10x^2-42x-2=0

a = -10; b = -42; c = -2;
Δ = b2-4ac
Δ = -422-4·(-10)·(-2)
Δ = 1684
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:

$\sqrt{\Delta}=\sqrt{1684}=\sqrt{4*421}=\sqrt{4}*\sqrt{421}=2\sqrt{421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{421}}{2*-10}=\frac{42-2\sqrt{421}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{421}}{2*-10}=\frac{42+2\sqrt{421}}{-20}
$