6(6x-5)X=7

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



6(6x-5)x=7
We move all terms to the left:
6(6x-5)x-(7)=0
We multiply parentheses
36x^2-30x-7=0
a = 36; b = -30; c = -7;
Δ = b2-4ac
Δ = -302-4·36·(-7)
Δ = 1908
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:
$\sqrt{\Delta}=\sqrt{1908}=\sqrt{36*53}=\sqrt{36}*\sqrt{53}=6\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{53}}{2*36}=\frac{30-6\sqrt{53}}{72} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{53}}{2*36}=\frac{30+6\sqrt{53}}{72} $

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