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(13-2x)(10-2x)=420
We move all terms to the left:
(13-2x)(10-2x)-(420)=0
We add all the numbers together, and all the variables
(-2x+13)(-2x+10)-420=0
We multiply parentheses ..
(+4x^2-20x-26x+130)-420=0
We get rid of parentheses
4x^2-20x-26x+130-420=0
We add all the numbers together, and all the variables
4x^2-46x-290=0
a = 4; b = -46; c = -290;
Δ = b2-4ac
Δ = -462-4·4·(-290)
Δ = 6756
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6756}=\sqrt{4*1689}=\sqrt{4}*\sqrt{1689}=2\sqrt{1689}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{1689}}{2*4}=\frac{46-2\sqrt{1689}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{1689}}{2*4}=\frac{46+2\sqrt{1689}}{8} $
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