5x^2-90=10+4x

Solution for 5x^2-90=10+4x equation:

5x^2-90=10+4x

We move all terms to the left:

5x^2-90-(10+4x)=0

We add all the numbers together, and all the variables

5x^2-(4x+10)-90=0

We get rid of parentheses

5x^2-4x-10-90=0

We add all the numbers together, and all the variables

5x^2-4x-100=0

a = 5; b = -4; c = -100;
Δ = b2-4ac
Δ = -42-4·5·(-100)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12\sqrt{14}}{2*5}=\frac{4-12\sqrt{14}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12\sqrt{14}}{2*5}=\frac{4+12\sqrt{14}}{10}
$