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.5x(x-10)=34+7x
We move all terms to the left:
.5x(x-10)-(34+7x)=0
We add all the numbers together, and all the variables
.5x(x-10)-(7x+34)=0
We multiply parentheses
x^2-10x-(7x+34)=0
We get rid of parentheses
x^2-10x-7x-34=0
We add all the numbers together, and all the variables
x^2-17x-34=0
a = 1; b = -17; c = -34;
Δ = b2-4ac
Δ = -172-4·1·(-34)
Δ = 425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-5\sqrt{17}}{2*1}=\frac{17-5\sqrt{17}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+5\sqrt{17}}{2*1}=\frac{17+5\sqrt{17}}{2} $
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