6x(x-5)=7(x-7)+5

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

6x(x-5)=7(x-7)+5

We move all terms to the left:

6x(x-5)-(7(x-7)+5)=0

We multiply parentheses

6x^2-30x-(7(x-7)+5)=0


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

7(x-7)+5

We multiply parentheses

7x-49+5

We add all the numbers together, and all the variables

7x-44

Back to the equation:

-(7x-44)


We get rid of parentheses

6x^2-30x-7x+44=0

We add all the numbers together, and all the variables

6x^2-37x+44=0

a = 6; b = -37; c = +44;
Δ = b2-4ac
Δ = -372-4·6·44
Δ = 313
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{313}}{2*6}=\frac{37-\sqrt{313}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{313}}{2*6}=\frac{37+\sqrt{313}}{12}
$