3(x-7)5x=6(8x-3)

Solution for 3(x-7)5x=6(8x-3) equation:

3(x-7)5x=6(8x-3)

We move all terms to the left:

3(x-7)5x-(6(8x-3))=0

We multiply parentheses

15x^2-105x-(6(8x-3))=0


We calculate terms in parentheses: -(6(8x-3)), so:

6(8x-3)

We multiply parentheses

48x-18

Back to the equation:

-(48x-18)


We get rid of parentheses

15x^2-105x-48x+18=0

We add all the numbers together, and all the variables

15x^2-153x+18=0

a = 15; b = -153; c = +18;
Δ = b2-4ac
Δ = -1532-4·15·18
Δ = 22329
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:

$\sqrt{\Delta}=\sqrt{22329}=\sqrt{9*2481}=\sqrt{9}*\sqrt{2481}=3\sqrt{2481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-153)-3\sqrt{2481}}{2*15}=\frac{153-3\sqrt{2481}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-153)+3\sqrt{2481}}{2*15}=\frac{153+3\sqrt{2481}}{30}
$