5x(6x-1)=(10-7)(3x+1)

Solution for 5x(6x-1)=(10-7)(3x+1) equation:

5x(6x-1)=(10-7)(3x+1)

We move all terms to the left:

5x(6x-1)-((10-7)(3x+1))=0

We add all the numbers together, and all the variables

5x(6x-1)-(3(3x+1))=0

We multiply parentheses

30x^2-5x-(3(3x+1))=0


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

3(3x+1)

We multiply parentheses

9x+3

Back to the equation:

-(9x+3)


We get rid of parentheses

30x^2-5x-9x-3=0

We add all the numbers together, and all the variables

30x^2-14x-3=0

a = 30; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·30·(-3)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{139}}{2*30}=\frac{14-2\sqrt{139}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{139}}{2*30}=\frac{14+2\sqrt{139}}{60}
$