(3x+7)(2x-3)=13

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Solution for (3x+7)(2x-3)=13 equation:



(3x+7)(2x-3)=13
We move all terms to the left:
(3x+7)(2x-3)-(13)=0
We multiply parentheses ..
(+6x^2-9x+14x-21)-13=0
We get rid of parentheses
6x^2-9x+14x-21-13=0
We add all the numbers together, and all the variables
6x^2+5x-34=0
a = 6; b = 5; c = -34;
Δ = b2-4ac
Δ = 52-4·6·(-34)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*6}=\frac{-34}{12} =-2+5/6 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*6}=\frac{24}{12} =2 $

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