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(21x-1)(8x+7)=x
We move all terms to the left:
(21x-1)(8x+7)-(x)=0
We add all the numbers together, and all the variables
-1x+(21x-1)(8x+7)=0
We multiply parentheses ..
(+168x^2+147x-8x-7)-1x=0
We get rid of parentheses
168x^2+147x-8x-1x-7=0
We add all the numbers together, and all the variables
168x^2+138x-7=0
a = 168; b = 138; c = -7;
Δ = b2-4ac
Δ = 1382-4·168·(-7)
Δ = 23748
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23748}=\sqrt{4*5937}=\sqrt{4}*\sqrt{5937}=2\sqrt{5937}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(138)-2\sqrt{5937}}{2*168}=\frac{-138-2\sqrt{5937}}{336} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(138)+2\sqrt{5937}}{2*168}=\frac{-138+2\sqrt{5937}}{336} $
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