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(2x+7)(4x-7)=x
We move all terms to the left:
(2x+7)(4x-7)-(x)=0
We add all the numbers together, and all the variables
-1x+(2x+7)(4x-7)=0
We multiply parentheses ..
(+8x^2-14x+28x-49)-1x=0
We get rid of parentheses
8x^2-14x+28x-1x-49=0
We add all the numbers together, and all the variables
8x^2+13x-49=0
a = 8; b = 13; c = -49;
Δ = b2-4ac
Δ = 132-4·8·(-49)
Δ = 1737
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1737}=\sqrt{9*193}=\sqrt{9}*\sqrt{193}=3\sqrt{193}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{193}}{2*8}=\frac{-13-3\sqrt{193}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{193}}{2*8}=\frac{-13+3\sqrt{193}}{16} $
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