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2x(3x+5)=180
We move all terms to the left:
2x(3x+5)-(180)=0
We multiply parentheses
6x^2+10x-180=0
a = 6; b = 10; c = -180;
Δ = b2-4ac
Δ = 102-4·6·(-180)
Δ = 4420
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4420}=\sqrt{4*1105}=\sqrt{4}*\sqrt{1105}=2\sqrt{1105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{1105}}{2*6}=\frac{-10-2\sqrt{1105}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{1105}}{2*6}=\frac{-10+2\sqrt{1105}}{12} $
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