4x^2-12x+10=37/4

Solution for 4x^2-12x+10=37/4 equation:

4x^2-12x+10=37/4

We move all terms to the left:

4x^2-12x+10-(37/4)=0

We add all the numbers together, and all the variables

4x^2-12x+10-(+37/4)=0

We get rid of parentheses

4x^2-12x+10-37/4=0

We multiply all the terms by the denominator


4x^2*4-12x*4-37+10*4=0

We add all the numbers together, and all the variables

4x^2*4-12x*4+3=0

Wy multiply elements

16x^2-48x+3=0

a = 16; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·16·3
Δ = 2112
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:

$\sqrt{\Delta}=\sqrt{2112}=\sqrt{64*33}=\sqrt{64}*\sqrt{33}=8\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{33}}{2*16}=\frac{48-8\sqrt{33}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{33}}{2*16}=\frac{48+8\sqrt{33}}{32}
$