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2x(3x-1)=7x+6-5x
We move all terms to the left:
2x(3x-1)-(7x+6-5x)=0
We add all the numbers together, and all the variables
2x(3x-1)-(2x+6)=0
We multiply parentheses
6x^2-2x-(2x+6)=0
We get rid of parentheses
6x^2-2x-2x-6=0
We add all the numbers together, and all the variables
6x^2-4x-6=0
a = 6; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·6·(-6)
Δ = 160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*6}=\frac{4-4\sqrt{10}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*6}=\frac{4+4\sqrt{10}}{12} $
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