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19x^2=15x+5
We move all terms to the left:
19x^2-(15x+5)=0
We get rid of parentheses
19x^2-15x-5=0
a = 19; b = -15; c = -5;
Δ = b2-4ac
Δ = -152-4·19·(-5)
Δ = 605
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{605}=\sqrt{121*5}=\sqrt{121}*\sqrt{5}=11\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-11\sqrt{5}}{2*19}=\frac{15-11\sqrt{5}}{38} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+11\sqrt{5}}{2*19}=\frac{15+11\sqrt{5}}{38} $
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