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6(3x-7)7x=13
We move all terms to the left:
6(3x-7)7x-(13)=0
We multiply parentheses
126x^2-294x-13=0
a = 126; b = -294; c = -13;
Δ = b2-4ac
Δ = -2942-4·126·(-13)
Δ = 92988
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{92988}=\sqrt{324*287}=\sqrt{324}*\sqrt{287}=18\sqrt{287}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-18\sqrt{287}}{2*126}=\frac{294-18\sqrt{287}}{252} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+18\sqrt{287}}{2*126}=\frac{294+18\sqrt{287}}{252} $
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