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5x+26+38x(x+2)=69
We move all terms to the left:
5x+26+38x(x+2)-(69)=0
We add all the numbers together, and all the variables
5x+38x(x+2)-43=0
We multiply parentheses
38x^2+5x+76x-43=0
We add all the numbers together, and all the variables
38x^2+81x-43=0
a = 38; b = 81; c = -43;
Δ = b2-4ac
Δ = 812-4·38·(-43)
Δ = 13097
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-\sqrt{13097}}{2*38}=\frac{-81-\sqrt{13097}}{76} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+\sqrt{13097}}{2*38}=\frac{-81+\sqrt{13097}}{76} $
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