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(4x-3)(2x+5)+114=180
We move all terms to the left:
(4x-3)(2x+5)+114-(180)=0
We add all the numbers together, and all the variables
(4x-3)(2x+5)-66=0
We multiply parentheses ..
(+8x^2+20x-6x-15)-66=0
We get rid of parentheses
8x^2+20x-6x-15-66=0
We add all the numbers together, and all the variables
8x^2+14x-81=0
a = 8; b = 14; c = -81;
Δ = b2-4ac
Δ = 142-4·8·(-81)
Δ = 2788
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2788}=\sqrt{4*697}=\sqrt{4}*\sqrt{697}=2\sqrt{697}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{697}}{2*8}=\frac{-14-2\sqrt{697}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{697}}{2*8}=\frac{-14+2\sqrt{697}}{16} $
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