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12x+10x(26-x)=290
We move all terms to the left:
12x+10x(26-x)-(290)=0
We add all the numbers together, and all the variables
12x+10x(-1x+26)-290=0
We multiply parentheses
-10x^2+12x+260x-290=0
We add all the numbers together, and all the variables
-10x^2+272x-290=0
a = -10; b = 272; c = -290;
Δ = b2-4ac
Δ = 2722-4·(-10)·(-290)
Δ = 62384
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{62384}=\sqrt{16*3899}=\sqrt{16}*\sqrt{3899}=4\sqrt{3899}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-4\sqrt{3899}}{2*-10}=\frac{-272-4\sqrt{3899}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+4\sqrt{3899}}{2*-10}=\frac{-272+4\sqrt{3899}}{-20} $
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