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x+6-(2x+7)3x=-9
We move all terms to the left:
x+6-(2x+7)3x-(-9)=0
We add all the numbers together, and all the variables
x-(2x+7)3x+15=0
We multiply parentheses
-6x^2+x-21x+15=0
We add all the numbers together, and all the variables
-6x^2-20x+15=0
a = -6; b = -20; c = +15;
Δ = b2-4ac
Δ = -202-4·(-6)·15
Δ = 760
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{190}}{2*-6}=\frac{20-2\sqrt{190}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{190}}{2*-6}=\frac{20+2\sqrt{190}}{-12} $
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