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(2x+7)(3x+2)=x
We move all terms to the left:
(2x+7)(3x+2)-(x)=0
We add all the numbers together, and all the variables
-1x+(2x+7)(3x+2)=0
We multiply parentheses ..
(+6x^2+4x+21x+14)-1x=0
We get rid of parentheses
6x^2+4x+21x-1x+14=0
We add all the numbers together, and all the variables
6x^2+24x+14=0
a = 6; b = 24; c = +14;
Δ = b2-4ac
Δ = 242-4·6·14
Δ = 240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{15}}{2*6}=\frac{-24-4\sqrt{15}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{15}}{2*6}=\frac{-24+4\sqrt{15}}{12} $
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