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x(2x+3)=377
We move all terms to the left:
x(2x+3)-(377)=0
We multiply parentheses
2x^2+3x-377=0
a = 2; b = 3; c = -377;
Δ = b2-4ac
Δ = 32-4·2·(-377)
Δ = 3025
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{3025}=55$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-55}{2*2}=\frac{-58}{4} =-14+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+55}{2*2}=\frac{52}{4} =13 $
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