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(3x+5)(5x+7)=90
We move all terms to the left:
(3x+5)(5x+7)-(90)=0
We multiply parentheses ..
(+15x^2+21x+25x+35)-90=0
We get rid of parentheses
15x^2+21x+25x+35-90=0
We add all the numbers together, and all the variables
15x^2+46x-55=0
a = 15; b = 46; c = -55;
Δ = b2-4ac
Δ = 462-4·15·(-55)
Δ = 5416
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5416}=\sqrt{4*1354}=\sqrt{4}*\sqrt{1354}=2\sqrt{1354}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{1354}}{2*15}=\frac{-46-2\sqrt{1354}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{1354}}{2*15}=\frac{-46+2\sqrt{1354}}{30} $
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