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5x^2+(10+x)x+2=0
We add all the numbers together, and all the variables
5x^2+(x+10)x+2=0
We multiply parentheses
5x^2+x^2+10x+2=0
We add all the numbers together, and all the variables
6x^2+10x+2=0
a = 6; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·6·2
Δ = 52
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*6}=\frac{-10-2\sqrt{13}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*6}=\frac{-10+2\sqrt{13}}{12} $
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