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5x(2x+3)=180
We move all terms to the left:
5x(2x+3)-(180)=0
We multiply parentheses
10x^2+15x-180=0
a = 10; b = 15; c = -180;
Δ = b2-4ac
Δ = 152-4·10·(-180)
Δ = 7425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7425}=\sqrt{225*33}=\sqrt{225}*\sqrt{33}=15\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15\sqrt{33}}{2*10}=\frac{-15-15\sqrt{33}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15\sqrt{33}}{2*10}=\frac{-15+15\sqrt{33}}{20} $
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