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4X^2+12X=-48X+159
We move all terms to the left:
4X^2+12X-(-48X+159)=0
We get rid of parentheses
4X^2+12X+48X-159=0
We add all the numbers together, and all the variables
4X^2+60X-159=0
a = 4; b = 60; c = -159;
Δ = b2-4ac
Δ = 602-4·4·(-159)
Δ = 6144
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-32\sqrt{6}}{2*4}=\frac{-60-32\sqrt{6}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+32\sqrt{6}}{2*4}=\frac{-60+32\sqrt{6}}{8} $
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