6(3x-5-)7x=25

Solution for 6(3x-5-)7x=25 equation:

6(3x-5-)7x=25

We move all terms to the left:

6(3x-5-)7x-(25)=0

We add all the numbers together, and all the variables

6(+3x)7x-25=0

We multiply parentheses

126x^2-25=0

a = 126; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·126·(-25)
Δ = 12600
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:

$\sqrt{\Delta}=\sqrt{12600}=\sqrt{900*14}=\sqrt{900}*\sqrt{14}=30\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{14}}{2*126}=\frac{0-30\sqrt{14}}{252}
=-\frac{30\sqrt{14}}{252}
=-\frac{5\sqrt{14}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{14}}{2*126}=\frac{0+30\sqrt{14}}{252}
=\frac{30\sqrt{14}}{252}
=\frac{5\sqrt{14}}{42}
$