6-5x(3x-4)=-34

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Solution for 6-5x(3x-4)=-34 equation:



6-5x(3x-4)=-34
We move all terms to the left:
6-5x(3x-4)-(-34)=0
We add all the numbers together, and all the variables
-5x(3x-4)+40=0
We multiply parentheses
-15x^2+20x+40=0
a = -15; b = 20; c = +40;
Δ = b2-4ac
Δ = 202-4·(-15)·40
Δ = 2800
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:
$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{7}}{2*-15}=\frac{-20-20\sqrt{7}}{-30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{7}}{2*-15}=\frac{-20+20\sqrt{7}}{-30} $

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