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(4x-13)(x+53)=180
We move all terms to the left:
(4x-13)(x+53)-(180)=0
We multiply parentheses ..
(+4x^2+212x-13x-689)-180=0
We get rid of parentheses
4x^2+212x-13x-689-180=0
We add all the numbers together, and all the variables
4x^2+199x-869=0
a = 4; b = 199; c = -869;
Δ = b2-4ac
Δ = 1992-4·4·(-869)
Δ = 53505
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{53505}=\sqrt{9*5945}=\sqrt{9}*\sqrt{5945}=3\sqrt{5945}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(199)-3\sqrt{5945}}{2*4}=\frac{-199-3\sqrt{5945}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(199)+3\sqrt{5945}}{2*4}=\frac{-199+3\sqrt{5945}}{8} $
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