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13x(10x+21)=90
We move all terms to the left:
13x(10x+21)-(90)=0
We multiply parentheses
130x^2+273x-90=0
a = 130; b = 273; c = -90;
Δ = b2-4ac
Δ = 2732-4·130·(-90)
Δ = 121329
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{121329}=\sqrt{9*13481}=\sqrt{9}*\sqrt{13481}=3\sqrt{13481}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(273)-3\sqrt{13481}}{2*130}=\frac{-273-3\sqrt{13481}}{260} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(273)+3\sqrt{13481}}{2*130}=\frac{-273+3\sqrt{13481}}{260} $
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