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5x(11x-2)=155
We move all terms to the left:
5x(11x-2)-(155)=0
We multiply parentheses
55x^2-10x-155=0
a = 55; b = -10; c = -155;
Δ = b2-4ac
Δ = -102-4·55·(-155)
Δ = 34200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{34200}=\sqrt{900*38}=\sqrt{900}*\sqrt{38}=30\sqrt{38}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30\sqrt{38}}{2*55}=\frac{10-30\sqrt{38}}{110} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30\sqrt{38}}{2*55}=\frac{10+30\sqrt{38}}{110} $
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