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6(5x+9)-(x^2-5)=x
We move all terms to the left:
6(5x+9)-(x^2-5)-(x)=0
We add all the numbers together, and all the variables
-1x+6(5x+9)-(x^2-5)=0
We multiply parentheses
-1x+30x-(x^2-5)+54=0
We get rid of parentheses
-x^2-1x+30x+5+54=0
We add all the numbers together, and all the variables
-1x^2+29x+59=0
a = -1; b = 29; c = +59;
Δ = b2-4ac
Δ = 292-4·(-1)·59
Δ = 1077
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{1077}}{2*-1}=\frac{-29-\sqrt{1077}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{1077}}{2*-1}=\frac{-29+\sqrt{1077}}{-2} $
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