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18x^2+3x=5x+26
We move all terms to the left:
18x^2+3x-(5x+26)=0
We get rid of parentheses
18x^2+3x-5x-26=0
We add all the numbers together, and all the variables
18x^2-2x-26=0
a = 18; b = -2; c = -26;
Δ = b2-4ac
Δ = -22-4·18·(-26)
Δ = 1876
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{469}}{2*18}=\frac{2-2\sqrt{469}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{469}}{2*18}=\frac{2+2\sqrt{469}}{36} $
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