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(6x+7)(7x-13)=x
We move all terms to the left:
(6x+7)(7x-13)-(x)=0
We add all the numbers together, and all the variables
-1x+(6x+7)(7x-13)=0
We multiply parentheses ..
(+42x^2-78x+49x-91)-1x=0
We get rid of parentheses
42x^2-78x+49x-1x-91=0
We add all the numbers together, and all the variables
42x^2-30x-91=0
a = 42; b = -30; c = -91;
Δ = b2-4ac
Δ = -302-4·42·(-91)
Δ = 16188
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16188}=\sqrt{4*4047}=\sqrt{4}*\sqrt{4047}=2\sqrt{4047}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{4047}}{2*42}=\frac{30-2\sqrt{4047}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{4047}}{2*42}=\frac{30+2\sqrt{4047}}{84} $
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