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135=4x+x^2
We move all terms to the left:
135-(4x+x^2)=0
We get rid of parentheses
-x^2-4x+135=0
We add all the numbers together, and all the variables
-1x^2-4x+135=0
a = -1; b = -4; c = +135;
Δ = b2-4ac
Δ = -42-4·(-1)·135
Δ = 556
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{139}}{2*-1}=\frac{4-2\sqrt{139}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{139}}{2*-1}=\frac{4+2\sqrt{139}}{-2} $
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