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x+x-8+10+5x(x-8)=151
We move all terms to the left:
x+x-8+10+5x(x-8)-(151)=0
We add all the numbers together, and all the variables
2x+5x(x-8)-149=0
We multiply parentheses
5x^2+2x-40x-149=0
We add all the numbers together, and all the variables
5x^2-38x-149=0
a = 5; b = -38; c = -149;
Δ = b2-4ac
Δ = -382-4·5·(-149)
Δ = 4424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4424}=\sqrt{4*1106}=\sqrt{4}*\sqrt{1106}=2\sqrt{1106}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{1106}}{2*5}=\frac{38-2\sqrt{1106}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{1106}}{2*5}=\frac{38+2\sqrt{1106}}{10} $
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