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7x(4x-9)=26+6x
We move all terms to the left:
7x(4x-9)-(26+6x)=0
We add all the numbers together, and all the variables
7x(4x-9)-(6x+26)=0
We multiply parentheses
28x^2-63x-(6x+26)=0
We get rid of parentheses
28x^2-63x-6x-26=0
We add all the numbers together, and all the variables
28x^2-69x-26=0
a = 28; b = -69; c = -26;
Δ = b2-4ac
Δ = -692-4·28·(-26)
Δ = 7673
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{-(-69)-\sqrt{7673}}{2*28}=\frac{69-\sqrt{7673}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{7673}}{2*28}=\frac{69+\sqrt{7673}}{56} $
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