(3x-4)(7x-9)=10

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Solution for (3x-4)(7x-9)=10 equation:



(3x-4)(7x-9)=10
We move all terms to the left:
(3x-4)(7x-9)-(10)=0
We multiply parentheses ..
(+21x^2-27x-28x+36)-10=0
We get rid of parentheses
21x^2-27x-28x+36-10=0
We add all the numbers together, and all the variables
21x^2-55x+26=0
a = 21; b = -55; c = +26;
Δ = b2-4ac
Δ = -552-4·21·26
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-29}{2*21}=\frac{26}{42} =13/21 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+29}{2*21}=\frac{84}{42} =2 $

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