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-23x-6x(5x-41)=259-41x
We move all terms to the left:
-23x-6x(5x-41)-(259-41x)=0
We add all the numbers together, and all the variables
-23x-6x(5x-41)-(-41x+259)=0
We multiply parentheses
-30x^2-23x+246x-(-41x+259)=0
We get rid of parentheses
-30x^2-23x+246x+41x-259=0
We add all the numbers together, and all the variables
-30x^2+264x-259=0
a = -30; b = 264; c = -259;
Δ = b2-4ac
Δ = 2642-4·(-30)·(-259)
Δ = 38616
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{38616}=\sqrt{4*9654}=\sqrt{4}*\sqrt{9654}=2\sqrt{9654}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(264)-2\sqrt{9654}}{2*-30}=\frac{-264-2\sqrt{9654}}{-60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(264)+2\sqrt{9654}}{2*-30}=\frac{-264+2\sqrt{9654}}{-60} $
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