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(10x-13)(3x+22)=x
We move all terms to the left:
(10x-13)(3x+22)-(x)=0
We add all the numbers together, and all the variables
-1x+(10x-13)(3x+22)=0
We multiply parentheses ..
(+30x^2+220x-39x-286)-1x=0
We get rid of parentheses
30x^2+220x-39x-1x-286=0
We add all the numbers together, and all the variables
30x^2+180x-286=0
a = 30; b = 180; c = -286;
Δ = b2-4ac
Δ = 1802-4·30·(-286)
Δ = 66720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{66720}=\sqrt{16*4170}=\sqrt{16}*\sqrt{4170}=4\sqrt{4170}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{4170}}{2*30}=\frac{-180-4\sqrt{4170}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{4170}}{2*30}=\frac{-180+4\sqrt{4170}}{60} $
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