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(x)(5x+13)=550
We move all terms to the left:
(x)(5x+13)-(550)=0
We multiply parentheses
5x^2+13x-550=0
a = 5; b = 13; c = -550;
Δ = b2-4ac
Δ = 132-4·5·(-550)
Δ = 11169
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11169}=\sqrt{9*1241}=\sqrt{9}*\sqrt{1241}=3\sqrt{1241}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{1241}}{2*5}=\frac{-13-3\sqrt{1241}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{1241}}{2*5}=\frac{-13+3\sqrt{1241}}{10} $
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