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(31x+4)(9x+6)=90
We move all terms to the left:
(31x+4)(9x+6)-(90)=0
We multiply parentheses ..
(+279x^2+186x+36x+24)-90=0
We get rid of parentheses
279x^2+186x+36x+24-90=0
We add all the numbers together, and all the variables
279x^2+222x-66=0
a = 279; b = 222; c = -66;
Δ = b2-4ac
Δ = 2222-4·279·(-66)
Δ = 122940
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{122940}=\sqrt{36*3415}=\sqrt{36}*\sqrt{3415}=6\sqrt{3415}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(222)-6\sqrt{3415}}{2*279}=\frac{-222-6\sqrt{3415}}{558} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(222)+6\sqrt{3415}}{2*279}=\frac{-222+6\sqrt{3415}}{558} $
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