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5x(3x+5)=690
We move all terms to the left:
5x(3x+5)-(690)=0
We multiply parentheses
15x^2+25x-690=0
a = 15; b = 25; c = -690;
Δ = b2-4ac
Δ = 252-4·15·(-690)
Δ = 42025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{42025}=205$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-205}{2*15}=\frac{-230}{30} =-7+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+205}{2*15}=\frac{180}{30} =6 $
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