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5x(3x-2)-2=4x
We move all terms to the left:
5x(3x-2)-2-(4x)=0
We add all the numbers together, and all the variables
-4x+5x(3x-2)-2=0
We multiply parentheses
15x^2-4x-10x-2=0
We add all the numbers together, and all the variables
15x^2-14x-2=0
a = 15; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·15·(-2)
Δ = 316
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{79}}{2*15}=\frac{14-2\sqrt{79}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{79}}{2*15}=\frac{14+2\sqrt{79}}{30} $
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