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(4x+10)(3x+42)=180
We move all terms to the left:
(4x+10)(3x+42)-(180)=0
We multiply parentheses ..
(+12x^2+168x+30x+420)-180=0
We get rid of parentheses
12x^2+168x+30x+420-180=0
We add all the numbers together, and all the variables
12x^2+198x+240=0
a = 12; b = 198; c = +240;
Δ = b2-4ac
Δ = 1982-4·12·240
Δ = 27684
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{27684}=\sqrt{36*769}=\sqrt{36}*\sqrt{769}=6\sqrt{769}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-6\sqrt{769}}{2*12}=\frac{-198-6\sqrt{769}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+6\sqrt{769}}{2*12}=\frac{-198+6\sqrt{769}}{24} $
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