2x(3X+4)=7

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Solution for 2x(3X+4)=7 equation:



2x(3x+4)=7
We move all terms to the left:
2x(3x+4)-(7)=0
We multiply parentheses
6x^2+8x-7=0
a = 6; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·6·(-7)
Δ = 232
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:
$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{58}}{2*6}=\frac{-8-2\sqrt{58}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{58}}{2*6}=\frac{-8+2\sqrt{58}}{12} $

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