5x(x-1)+7x=(6x-1)(2x+3)

Solution for 5x(x-1)+7x=(6x-1)(2x+3) equation:

5x(x-1)+7x=(6x-1)(2x+3)

We move all terms to the left:

5x(x-1)+7x-((6x-1)(2x+3))=0

We add all the numbers together, and all the variables

7x+5x(x-1)-((6x-1)(2x+3))=0

We multiply parentheses

5x^2+7x-5x-((6x-1)(2x+3))=0

We multiply parentheses ..

5x^2-((+12x^2+18x-2x-3))+7x-5x=0


We calculate terms in parentheses: -((+12x^2+18x-2x-3)), so:

(+12x^2+18x-2x-3)

We get rid of parentheses

12x^2+18x-2x-3

We add all the numbers together, and all the variables

12x^2+16x-3

Back to the equation:

-(12x^2+16x-3)


We add all the numbers together, and all the variables

5x^2+2x-(12x^2+16x-3)=0

We get rid of parentheses

5x^2-12x^2+2x-16x+3=0

We add all the numbers together, and all the variables

-7x^2-14x+3=0

a = -7; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·(-7)·3
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{70}}{2*-7}=\frac{14-2\sqrt{70}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{70}}{2*-7}=\frac{14+2\sqrt{70}}{-14}
$