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2x(2x+1)=26
We move all terms to the left:
2x(2x+1)-(26)=0
We multiply parentheses
4x^2+2x-26=0
a = 4; b = 2; c = -26;
Δ = b2-4ac
Δ = 22-4·4·(-26)
Δ = 420
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{105}}{2*4}=\frac{-2-2\sqrt{105}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{105}}{2*4}=\frac{-2+2\sqrt{105}}{8} $
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