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4(6x-5)6x=6-7x+5x-2
We move all terms to the left:
4(6x-5)6x-(6-7x+5x-2)=0
We add all the numbers together, and all the variables
4(6x-5)6x-(-2x+4)=0
We multiply parentheses
144x^2-120x-(-2x+4)=0
We get rid of parentheses
144x^2-120x+2x-4=0
We add all the numbers together, and all the variables
144x^2-118x-4=0
a = 144; b = -118; c = -4;
Δ = b2-4ac
Δ = -1182-4·144·(-4)
Δ = 16228
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16228}=\sqrt{4*4057}=\sqrt{4}*\sqrt{4057}=2\sqrt{4057}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-118)-2\sqrt{4057}}{2*144}=\frac{118-2\sqrt{4057}}{288} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118)+2\sqrt{4057}}{2*144}=\frac{118+2\sqrt{4057}}{288} $
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