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(4x+11)(5x+7)=90
We move all terms to the left:
(4x+11)(5x+7)-(90)=0
We multiply parentheses ..
(+20x^2+28x+55x+77)-90=0
We get rid of parentheses
20x^2+28x+55x+77-90=0
We add all the numbers together, and all the variables
20x^2+83x-13=0
a = 20; b = 83; c = -13;
Δ = b2-4ac
Δ = 832-4·20·(-13)
Δ = 7929
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7929}=\sqrt{9*881}=\sqrt{9}*\sqrt{881}=3\sqrt{881}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(83)-3\sqrt{881}}{2*20}=\frac{-83-3\sqrt{881}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(83)+3\sqrt{881}}{2*20}=\frac{-83+3\sqrt{881}}{40} $
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