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22+3x(+5x+8)=180
We move all terms to the left:
22+3x(+5x+8)-(180)=0
We add all the numbers together, and all the variables
3x(5x+8)+22-180=0
We add all the numbers together, and all the variables
3x(5x+8)-158=0
We multiply parentheses
15x^2+24x-158=0
a = 15; b = 24; c = -158;
Δ = b2-4ac
Δ = 242-4·15·(-158)
Δ = 10056
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10056}=\sqrt{4*2514}=\sqrt{4}*\sqrt{2514}=2\sqrt{2514}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{2514}}{2*15}=\frac{-24-2\sqrt{2514}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{2514}}{2*15}=\frac{-24+2\sqrt{2514}}{30} $
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