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(3x+20)(5x-8)=90
We move all terms to the left:
(3x+20)(5x-8)-(90)=0
We multiply parentheses ..
(+15x^2-24x+100x-160)-90=0
We get rid of parentheses
15x^2-24x+100x-160-90=0
We add all the numbers together, and all the variables
15x^2+76x-250=0
a = 15; b = 76; c = -250;
Δ = b2-4ac
Δ = 762-4·15·(-250)
Δ = 20776
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20776}=\sqrt{196*106}=\sqrt{196}*\sqrt{106}=14\sqrt{106}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-14\sqrt{106}}{2*15}=\frac{-76-14\sqrt{106}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+14\sqrt{106}}{2*15}=\frac{-76+14\sqrt{106}}{30} $
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