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(4x+3)(x-2)=90
We move all terms to the left:
(4x+3)(x-2)-(90)=0
We multiply parentheses ..
(+4x^2-8x+3x-6)-90=0
We get rid of parentheses
4x^2-8x+3x-6-90=0
We add all the numbers together, and all the variables
4x^2-5x-96=0
a = 4; b = -5; c = -96;
Δ = b2-4ac
Δ = -52-4·4·(-96)
Δ = 1561
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{1561}}{2*4}=\frac{5-\sqrt{1561}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1561}}{2*4}=\frac{5+\sqrt{1561}}{8} $
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