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-6x(x+7)=-4x-2
We move all terms to the left:
-6x(x+7)-(-4x-2)=0
We multiply parentheses
-6x^2-42x-(-4x-2)=0
We get rid of parentheses
-6x^2-42x+4x+2=0
We add all the numbers together, and all the variables
-6x^2-38x+2=0
a = -6; b = -38; c = +2;
Δ = b2-4ac
Δ = -382-4·(-6)·2
Δ = 1492
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1492}=\sqrt{4*373}=\sqrt{4}*\sqrt{373}=2\sqrt{373}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{373}}{2*-6}=\frac{38-2\sqrt{373}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{373}}{2*-6}=\frac{38+2\sqrt{373}}{-12} $
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