(9x-19)(10x-13)=0

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Solution for (9x-19)(10x-13)=0 equation:



(9x-19)(10x-13)=0
We multiply parentheses ..
(+90x^2-117x-190x+247)=0
We get rid of parentheses
90x^2-117x-190x+247=0
We add all the numbers together, and all the variables
90x^2-307x+247=0
a = 90; b = -307; c = +247;
Δ = b2-4ac
Δ = -3072-4·90·247
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-307)-73}{2*90}=\frac{234}{180} =1+3/10 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-307)+73}{2*90}=\frac{380}{180} =2+1/9 $

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