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800=(15+2x)(30+2x)
We move all terms to the left:
800-((15+2x)(30+2x))=0
We add all the numbers together, and all the variables
-((2x+15)(2x+30))+800=0
We multiply parentheses ..
-((+4x^2+60x+30x+450))+800=0
We calculate terms in parentheses: -((+4x^2+60x+30x+450)), so:We get rid of parentheses
(+4x^2+60x+30x+450)
We get rid of parentheses
4x^2+60x+30x+450
We add all the numbers together, and all the variables
4x^2+90x+450
Back to the equation:
-(4x^2+90x+450)
-4x^2-90x-450+800=0
We add all the numbers together, and all the variables
-4x^2-90x+350=0
a = -4; b = -90; c = +350;
Δ = b2-4ac
Δ = -902-4·(-4)·350
Δ = 13700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13700}=\sqrt{100*137}=\sqrt{100}*\sqrt{137}=10\sqrt{137}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10\sqrt{137}}{2*-4}=\frac{90-10\sqrt{137}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10\sqrt{137}}{2*-4}=\frac{90+10\sqrt{137}}{-8} $
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