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(4x+3)(x+12)=90
We move all terms to the left:
(4x+3)(x+12)-(90)=0
We multiply parentheses ..
(+4x^2+48x+3x+36)-90=0
We get rid of parentheses
4x^2+48x+3x+36-90=0
We add all the numbers together, and all the variables
4x^2+51x-54=0
a = 4; b = 51; c = -54;
Δ = b2-4ac
Δ = 512-4·4·(-54)
Δ = 3465
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3465}=\sqrt{9*385}=\sqrt{9}*\sqrt{385}=3\sqrt{385}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{385}}{2*4}=\frac{-51-3\sqrt{385}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{385}}{2*4}=\frac{-51+3\sqrt{385}}{8} $
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