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x(x-3)+x(x-4)=30-x
We move all terms to the left:
x(x-3)+x(x-4)-(30-x)=0
We add all the numbers together, and all the variables
x(x-3)+x(x-4)-(-1x+30)=0
We multiply parentheses
x^2+x^2-3x-4x-(-1x+30)=0
We get rid of parentheses
x^2+x^2-3x-4x+1x-30=0
We add all the numbers together, and all the variables
2x^2-6x-30=0
a = 2; b = -6; c = -30;
Δ = b2-4ac
Δ = -62-4·2·(-30)
Δ = 276
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{69}}{2*2}=\frac{6-2\sqrt{69}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{69}}{2*2}=\frac{6+2\sqrt{69}}{4} $
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