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(2x+3)(5x+3)=90
We move all terms to the left:
(2x+3)(5x+3)-(90)=0
We multiply parentheses ..
(+10x^2+6x+15x+9)-90=0
We get rid of parentheses
10x^2+6x+15x+9-90=0
We add all the numbers together, and all the variables
10x^2+21x-81=0
a = 10; b = 21; c = -81;
Δ = b2-4ac
Δ = 212-4·10·(-81)
Δ = 3681
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3681}=\sqrt{9*409}=\sqrt{9}*\sqrt{409}=3\sqrt{409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{409}}{2*10}=\frac{-21-3\sqrt{409}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{409}}{2*10}=\frac{-21+3\sqrt{409}}{20} $
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