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3x^2+5x-2=180
We move all terms to the left:
3x^2+5x-2-(180)=0
We add all the numbers together, and all the variables
3x^2+5x-182=0
a = 3; b = 5; c = -182;
Δ = b2-4ac
Δ = 52-4·3·(-182)
Δ = 2209
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{2209}=47$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-47}{2*3}=\frac{-52}{6} =-8+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+47}{2*3}=\frac{42}{6} =7 $
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