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90=(3x+2)(2x+18)
We move all terms to the left:
90-((3x+2)(2x+18))=0
We multiply parentheses ..
-((+6x^2+54x+4x+36))+90=0
We calculate terms in parentheses: -((+6x^2+54x+4x+36)), so:We get rid of parentheses
(+6x^2+54x+4x+36)
We get rid of parentheses
6x^2+54x+4x+36
We add all the numbers together, and all the variables
6x^2+58x+36
Back to the equation:
-(6x^2+58x+36)
-6x^2-58x-36+90=0
We add all the numbers together, and all the variables
-6x^2-58x+54=0
a = -6; b = -58; c = +54;
Δ = b2-4ac
Δ = -582-4·(-6)·54
Δ = 4660
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4660}=\sqrt{4*1165}=\sqrt{4}*\sqrt{1165}=2\sqrt{1165}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{1165}}{2*-6}=\frac{58-2\sqrt{1165}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{1165}}{2*-6}=\frac{58+2\sqrt{1165}}{-12} $
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