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(5x+11)(3x+7)=90
We move all terms to the left:
(5x+11)(3x+7)-(90)=0
We multiply parentheses ..
(+15x^2+35x+33x+77)-90=0
We get rid of parentheses
15x^2+35x+33x+77-90=0
We add all the numbers together, and all the variables
15x^2+68x-13=0
a = 15; b = 68; c = -13;
Δ = b2-4ac
Δ = 682-4·15·(-13)
Δ = 5404
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5404}=\sqrt{4*1351}=\sqrt{4}*\sqrt{1351}=2\sqrt{1351}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-2\sqrt{1351}}{2*15}=\frac{-68-2\sqrt{1351}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+2\sqrt{1351}}{2*15}=\frac{-68+2\sqrt{1351}}{30} $
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