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6x^2+19x+153x+5=0
We add all the numbers together, and all the variables
6x^2+172x+5=0
a = 6; b = 172; c = +5;
Δ = b2-4ac
Δ = 1722-4·6·5
Δ = 29464
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{29464}=\sqrt{4*7366}=\sqrt{4}*\sqrt{7366}=2\sqrt{7366}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(172)-2\sqrt{7366}}{2*6}=\frac{-172-2\sqrt{7366}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(172)+2\sqrt{7366}}{2*6}=\frac{-172+2\sqrt{7366}}{12} $
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