4x-3+312+14-10=245x+12-14x^2

Solution for 4x-3+312+14-10=245x+12-14x^2 equation:

4x-3+312+14-10=245x+12-14x^2

We move all terms to the left:

4x-3+312+14-10-(245x+12-14x^2)=0

We add all the numbers together, and all the variables

-(245x+12-14x^2)+4x+313=0

We get rid of parentheses

14x^2-245x+4x-12+313=0

We add all the numbers together, and all the variables

14x^2-241x+301=0

a = 14; b = -241; c = +301;
Δ = b2-4ac
Δ = -2412-4·14·301
Δ = 41225
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:

$\sqrt{\Delta}=\sqrt{41225}=\sqrt{25*1649}=\sqrt{25}*\sqrt{1649}=5\sqrt{1649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-241)-5\sqrt{1649}}{2*14}=\frac{241-5\sqrt{1649}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-241)+5\sqrt{1649}}{2*14}=\frac{241+5\sqrt{1649}}{28}
$