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5x(3x+2)=2
We move all terms to the left:
5x(3x+2)-(2)=0
We multiply parentheses
15x^2+10x-2=0
a = 15; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·15·(-2)
Δ = 220
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{55}}{2*15}=\frac{-10-2\sqrt{55}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{55}}{2*15}=\frac{-10+2\sqrt{55}}{30} $
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